L I C E N T I AT E T H E S I S
ISSN: 1402-1757 ISBN 978-91-7439-374-3 Luleå University of Technology 2011
Gerrit Holl Microwave and Infrared Remote Sensing of Ice Clouds: Measurements and Radiative Transfer Simulations
Department of Computer Science, Electrical and Space Engineering Division of Space Technology
Microwave and Infrared Remote Sensing of Ice Clouds: Measurements and Radiative Transfer Simulations
Gerrit Holl
Licentiate thesis
Microwave and infrared remote sensing of ice clouds: measurements and radiative transfer simulations
Gerrit Holl 16 January 2012 Department of Computer Science, Electrical and Space Engineering Division of Space Technology Graduate School of Space Technology Luleå University of Technology Rymdcampus 1 98 128 Kiruna, Sweden
Printed by Universitetstryckeriet, Luleå 2011 ISSN: 1402-1757 ISBN 978-91-7439-374-3 Luleå 2011 www.ltu.se
Abstract This licentiate thesis considers the combination of multiple instruments for remote sensing of the Earth atmosphere from space. The primary focus is on remote sensing of atmospheric ice. Ice clouds are important for the Earth’s radiation budget, but their properties are difficult to measure and therefore poorly known. A better quantification of ice clouds is needed to improve global climate models. This thesis introduces the reader to the subject and describes how to combine measurements and radiative transfer simulations in an attempt to improve our understanding. A major part of this work is the development of a toolkit to find co-incident measurements, or collocations, between any pair of down-looking satellite sensors. Firstly, this toolkit is used to collocate passive microwave and thermal infrared sensors on meteorological satellites with the Cloud Profiling Radar on CloudSat. With the resulting collocated dataset, the Ice Water Path (IWP) signal in passive thermal radiation is studied and an improved IWP retrieval is presented. The toolkit is also used to better characterise the bias between different copies of passive microwave radiometers on-board polar-orbiting operational satellites. For the Atmospheric Radiative Transfer Simulator (ARTS), version 2, an optimised frequency grid for infrared broadband simulations is shown to be applicable for cloudy simulations. This frequency grid can and will be used to study the IWP signal in thermal infrared radiances. An outlook on a comparison between collocations and simulations is presented in the thesis.
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Appended papers Paper I G. Holl, S. A. Buehler, B. Rydberg, and C. Jiménez. Collocating satellite-based radar and radiometer measurements – methodology and usage examples. Atmos. Meas. Tech., 3:693–708, 2010. doi: 10.5194/ amt-3-693-2010 Paper II V. O. John, G. Holl, S. A. Buehler, B. Candy, R. W. Saunders, and D. E. Parker. Understanding inter-satellite biases of microwave humidity sounders using global SNOs. J. Geophys. Res., 2011b. in press Paper III G. Holl, S. A. Buehler, J. Mendrok, and A. Kottayil. Simulating cloudy thermal infrared radiances with an optimised frequency grid in the radiative transfer model ARTS. J. Quant. Spectrosc. Radiat. Transfer, to be submitted
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Related papers • A. Kottayil, S. A. Buehler, V. O. John, L. M. Miloshevich, M. Milz, and G. Holl. On the importance of Vaisala RS92 radiosonde humidity corrections for a better agreement between measured and modeled satellite radiances. J. Atmos. Oceanic Technol., accepted 2011 • V. O. John, G. Holl, R. P. Allan, S. A. Buehler, D. E. Parker, and B. J. Soden. Clear-sky biases in satellite infra-red estimates of upper tropospheric humidity and its trends. J. Geophys. Res., 116:D14108, 2011a. doi: 10.1029/2010JD015355
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Contents
Abstract
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Appended papers
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Related papers
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Table of contents
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Acknowledgements
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Chapter 1 – Introduction 1.1 Climate change . . . . 1.2 Remote sensing . . . . 1.3 Clouds . . . . . . . . . 1.4 Aims and ways . . . . 1.4.1 Tools . . . . . . 1.4.2 Applications . .
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Chapter 2 – Remote sensing 2.1 Electromagnetic radiation 2.2 Sensor considerations . . . 2.2.1 Imaging . . . . . . 2.2.2 Sounding . . . . . 2.2.3 Scattering . . . . . 2.2.4 Orbits . . . . . . . 2.3 Thermal infrared . . . . . 2.3.1 HIRS . . . . . . . . 2.3.2 AVHRR . . . . . . 2.4 Passive microwave . . . . . 2.4.1 MHS and AMSU-B 2.5 Radar . . . . . . . . . . .
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2.5.1 CloudSat and the A-Train Collocations . . . . . . . . . . . . 2.6.1 Criteria . . . . . . . . . . 2.6.2 Method . . . . . . . . . . 2.6.3 Collocated datasets . . . .
Chapter 3 – Ice clouds 3.1 Radiative effects . . . . . 3.2 Microphysical properties 3.3 Optical properties . . . . 3.4 Bulk physical properties
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Chapter 4 – Radiative transfer 4.1 Theory . . . . . . . . . . . . . . . . 4.1.1 Clear-sky radiative transfer 4.1.2 Particles . . . . . . . . . . . 4.2 Practical considerations . . . . . . 4.2.1 Sensors . . . . . . . . . . . . 4.2.2 Databases . . . . . . . . . . 4.2.3 Sources for profiles . . . . . 4.3 Retrieval development . . . . . . . 4.4 ARTS . . . . . . . . . . . . . . . . 4.4.1 Optimisations . . . . . . . . 4.4.2 Scattering . . . . . . . . . .
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Chapter 5 – This thesis 5.1 Paper summaries . 5.1.1 Paper I . . 5.1.2 Paper II . . 5.1.3 Paper III . 5.2 Outlook — Road to
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References
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Glossary
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Acronyms
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Paper I
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Paper II
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Paper III
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Acknowledgements Virtually no work done by a human being is ever done alone. Human work is cooperative and the work resulting in this thesis is no exception. Without help and encouragement of dozens of people throughout my life, this thesis would not exist. In these acknowledgements, I limit myself to the very basics, to people who have been of direct importance for myself as a person or for my scientific output. I would like to thank my supervisor, Stefan Buehler. From the very start when I joined the group as a part-time master student more than three years ago, your supervision has been dedicated and highly valuable. I appreciate this very much. Thanks! Scientific discussion is essential in all branches of academia. I am grateful for all the valuable input, in weekly group meetings or in smaller discussions, from all people in the research group: Stefan Buehler, Jana Mendrok, Thomas Kuhn, Mathias Milz, Salomon Eliasson, Ajil Kottayil, as well as former group members Isaac Moradi and Daniel Kreyling. Also a big thanks to Oliver Lemke, who has helped out with countless of smaller and larger computer-related issues. Scientific cooperation is not limited to my own group. Outside our own group, I would like to thank Carlos Jiménez, Bengt Rydberg, and Viju John for productive scientific cooperation. I am indebted also to my co-supervisor Patrick Eriksson. In the past years, I have had the opportunity to participate in various courses. I am grateful to the Swedish National Graduate School in Space Technology for organising a good share of those courses. Additionally, I would like to thank Utrecht University for the summer school in Physics of the Climate System in 2009, the European Space Agency for the summer school in Earth Observation and Modeling in 2010, and the Université Joseph Fourier with all co-organisers and co-sponsors for my chance to participate in the European Research Course on Atmospheres in 2011. Most recently, I have taken part in a small, unconventional, but very useful course called Utveckling av Grupp och Ledare. The value of this training for my further academic career and my further life can hardly be overestimated. My big xi
thanks to Kurt Pedersen for recommending me to take this course, to Luleå University of Technology for making it possible, and to the supervisors and participants in the course for making it a success. My thanks to the community for building and maintaining the Atmospheric Radiative Transfer Simulator along with the tools Atmlab and PyARTS. Additionally, a number of opensource software packages not developed at our group have proven invaluable in my work. For the scientific data analysis I have used Python, numpy, scipy, matplotlib, and countless of other, smaller packages that lie at the basis of the opensource software world that make using computers so much more pleasant and that have enhanced my productivity considerably. To write articles, to make presentations, and to design posters, LATEX and associated packages have been of great help. My gratitude to all people who have donated their time for developing opensource software, for writing documentation, and for helping out on forums and mailing-lists. Finally, I wish to express thanks to a number of people who have been valuable on a personal level. Thanks to my parents, Han and Tinelot, my sisters Elchien and Duveken; need I say why? Shortly before I accepted Stefans offer to become his PhD student, I met you, Catherine. I do not possess the words to describe how fortunate I have been, how fortunate that you have come into my life. Therefore, I will just finish by saying a big thank you for everything we have shared in the past, do share in the present, and will share in the future.
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Chapter 1 Introduction
1.1
Climate change
Planet Earth is the home of all humanity, a population of seven billion souls and ever increasing. We all live at the boundary between the solid Earth and the atmosphere that surrounds it. This atmosphere is highly dynamic, with pressure, humidity, and precipitation quickly varying in space and in time; this we experience as weather. Statistics of the weather in a specific region over a long period of time (typically thirty years) define the climate. The climate on planet Earth is changing. Measurements and models show that temperatures are increasing and precipitation patterns are changing (Trenberth et al., 2007). It is very likely that those changes are due to anthropogenic influences (Hegerl et al., 2007). Climate change has the potential to significantly affect our natural environment (Rosenzweig et al., 2007). Therefore, a good understanding of the climate system is imperative.
1.2
Remote sensing
To improve our understanding of climate, observations of many parameters are needed that a) span a long time range, b) have a good time resolution (high sampling frequency), c) have global coverage, d) have a good spatial resolution, and e) have a small error. Satellite measurements have the potential to fulfil criteria (c) and (d). In some cases, criterion (a) may also be fulfilled. Depending on the quantity measured, criterion (e) is hard to achieve with satellite measurements. Criterion (b) can conditionally be achieved with satellite measurements. Instruments on satellites in a geostationary 1
2
Introduction
orbit may have a time sampling as high as 15 minutes, whereas polar-orbiting satellites that measure only at nadir (such as CloudSat, discussed later in this thesis) may see the same place only at an interval of several weeks. For some measurements, the accuracy of satellite-based measurements can be as high as the accuracy of in situ measurements. For remote sensing of ice clouds, however, meeting criterion (e) is a challenge. Meeting criterion (c) with anything but satellite measurements is not feasible. Therefore, despite the potential challenges to achieve criterion (e), satellite measurements are our only hope to meet all 5 criteria (meeting criterion (a) should be only a matter of time).
1.3
Clouds
Clouds have a strong effect on the Earth radiation budget (Rogers and Yau, 1976). According to the Intergovernmental Panel on Climate Change (IPCC) 4th Assessment Report (AR4), “cloud feedbacks remain the largest source of uncertainty in climate sensitivity estimates” (Randall et al., 2007, Section 8.6.3.2). In climate models, the magnitude and the sign of the feedback is almost entirely dictated by model assumptions (Stephens, 2005). Therefore, there is a strong need for a better understanding of clouds. More information on clouds is given in chapter 3. Both modelling and measuring clouds is even more difficult if the cloud consists of ice. To successfully do either, accurate and independent knowledge of particle sizes and shapes is required. Currently, this requirement cannot be met, because no existing sensor can accurately measure shape, sizes, number density and mass density independently. Although this will not be solved with existing sensors, existing retrievals of cloud ice column mass density can be improved. This licentiate thesis describes how.
1.4
Aims and ways
This licentiate thesis shall be seen as a step toward an improved quantification of ice clouds from satellite measurements. The focus is on the column density of ice, or Ice Water Path (IWP). Quoting the introduction to Paper III: In estimates of the atmospheric column density of ice, IWP, models and measurements vary by up to an order of magnitude (Waliser et al., 2009) and show different spatial distributions (Eliasson et al., 2011). Therefore, there is a need for an improved IWP retrieval. (Paper III)
1.4. Aims and ways
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Ultimately, the aim of this work is to improve global climate models.
1.4.1
Tools
Two strategies are combined to work toward this improvement. Those are briefly introduced below, but described in more depth in section 2.6 and in chapter 4. 1.4.1.1
Collocations
A collocation is an event where different instruments remotely observe the same area (or volume) at approximately the same time. Collocations have advantages over using either instrument alone. For example, collocations between the CloudSat Cloud Profiling Radar (CPR) and National Oceanic and Atmospheric Administration (NOAA)-18 Microwave Humidity Sounder (MHS) can teach us how IWP affects radiances measured with MHS. Collocations are described in more detail in section 2.6 and in Paper I. 1.4.1.2
Radiative transfer
Radiative transfer is the modelling of the interaction of electromagnetic radiation with a medium or a surface. One example is the simulation of radiation emitted by the Earth’s surface and atmosphere and measured by a satellite. Many software models to perform such simulations exist. For example, with the Atmospheric Radiative Transfer Simulator (ARTS), satellite radiances in a cloudy atmosphere can be calculated (Eriksson et al., 2011a; Buehler et al., 2005). This too can teach us about the relation between cloud ice and radiances. The usage of ARTS in this thesis is described in detail in section 4.4.
1.4.2
Applications
As shown in Paper I, the collocation toolkit has already resulted in a new IWP product developed purely from collocations. This product was developed by collocating the CloudSat CPR IWP product with passive microwave radiances from NOAA-18 MHS and then training an Artificial Neural Network (ANN). This is described in detail in Paper I. However, both collocations and radiative transfer developed and applied for this thesis have uses beyond the primary aim of improving IWP retrievals. The collocations toolkit described in section 2.6 was initially developed to collocate the CloudSat CPR with MHS and Advanced Microwave Sounding
4
Introduction
Unit (AMSU)-B on-board NOAA and MetOp satellites. However, the code was designed to be flexible. This allows for numerous spin-off projects. John et al. (2011a) use the toolkit to collocate cloud-cleared data from the High resolution Infrared Radiation Sounder (HIRS) instrument with AMSU measurements, to investigate biases introduced by cloud-clearing in the climatology of Upper Tropospheric Humidity (UTH). In Paper II, nadir collocations (there referred to as simultaneous nadir overpasss (SNOs)) between different copies of AMSUB and MHS are used to find the latitudinal dependence of inter-satellite biases. Other projects using either the collocation toolkit or one of the resulting datasets are currently in various stages of development. The radiative transfer code used was available prior to the project or developed in parallel by others. However, small improvements to ARTS were made as part of the thesis project. Results obtained for the project, such as for Paper III, can also be applied in other contexts.
Chapter 2 Remote sensing
This chapter contains a brief introduction to those aspects of remote sensing relevant for this thesis. It does not aim to be complete and completely skips certain important aspects of (atmospheric) remote sensing. A more complete introduction can be found in Rees (2001) or any other textbook. This chapter does not address the problem of retrieving geophysical quantities from measurements. For a discussion on retrievals of cloud properties from remote sensing measurements, please refer to Stephens and Kummerow (2007) or to the theses by Eliasson (2011) or Rydberg (2010) and references therein. Earth observation from space has been a major motivation for the launch of satellites in the past half century. The first successful weather satellite was Television InfraRed Operational Sounder (TIROS)-1, launched 1 April 1960, less than three years after the launch of Sputnik marked the beginning of the space age in October 1957. The ability to directly image the Earth from space (Figure 2.1) marked a revolution in meteorology and climatol- Figure 2.1 – Photograph of a cyclone, ogy. Now, synoptic-scale weather sys- taken by TIROS-1 on 28 April 1960. tems could be directly observed from space. Furthermore, measurements became available on a global scale, providing information in areas far away from any weather stations. It is therefore 5
6 1 PHz visible
1 μm
Remote sensing
no surprise that after the launch of TIROS-1, dozens of Earth observation satellites have been launched and are operated by organisations around the world, with always new satellites and sensors in planning. For a history of past Earth observation sensors, the review papers of Smith et al. (1986) and Kidd et al. (2009) are valuable. Thies and Bendix (2011) discuss satellites to be launched in the near future.
100 THz
2.1
Electromagnetic radiation
HIRS-12 10 μm
AVHRR5
10 THz
Almost all Earth observation satellites, and all satellites observing the lower atmosphere, measure electromagnetic radiation. They do so at various frequencies throughout the spectrum, as illustrated by the graphic in the left margin. Electromagnetic radiation is emitted by any object with a non-zero absolute temperature, including the Earth atmosphere. For a blackbody, the energy emitted as a function of wavelength is described by Planck’s law, 2hf 3
Lf,p “
100 μm
hf
c2 pe kT ´ 1q
,
(2.1)
or, with wavelength rather than frequency, 1 THz submm
1 mm MHS3–5 100 GHz CPR
10 mm
10 GHz
2hc2 hc
λ5 pe λkT ´ 1q
.
(2.2)
Here, Lf,p is the spectral radiance in W sr´1 m´2 Hz´1 or equivalent (where Hz may be replaced by another spectral unit), h is the Planck constant with a value of 6.6261 ˆ 10´34 J s is the Planck constant, c “ 2.9979 ˆ 108 m s´1 is the propagation speed of electromagnetic radiation in vacuum, k “ 1.3807 ˆ 10´23 J K´1 is the Boltzmann constant, T is the absolute temperature in K, and λ is the wavelength in m. Figure 2.2 shows the blackbody curves for the Sun with an effective surface temperature of 5778 K and for the Earth at a surface temperature of 287 K, as well as Top Of Atmosphere (TOA) terrestrial radiation. Real bodies are not blackbodies, but emit at a certain emissivity , Lf “ pf qLf,p ,
PR
100 mm
Lλ,p “
or, Lλ “ pλqLλ,p .
(2.3)
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2.1. Electromagnetic radiation
normalised spectral irradiance “ ‰ W m´2 sr´1 μm´1
Atmospheric radiation
0.2
Earth blackbody body ((T “ 287 K)
Sun blackbody
window region
TOA spectral irradiance
UV
VIS 0.4
Near infrared nfrare 0.7
Teerrestriial infrared ed 3
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13
70
wavelength rμms
Figure 2.2 – Electromagnetic radiation as transmitted through the Earth’s atmosphere: solar and thermal radiation. The lines show blackbody curves, whereas the solid part shows what part of terrestrial radiation makes it through the atmosphere. The difference is absorbed by various gases. IR radiation is mostly absorbed by greenhouse gases such as water vapour and carbon dioxide.
For the Earth or an object at a similar temperature, the spectral radiance in W sr´1 m´2 Hz´1 emitted at the microwave wavelength of 20 GHz (1.54 cm) is approximately ten orders of magnitude less than the spectral radiance at the peak wavelength of 10.3 μm (Rees, 2001, page 27). It is not practical to express radiation in W sr´1 m´2 Hz´1 . This is one of the reasons that terrestrial radiation is commonly expressed in brightness temperature, Tb “
´
hc
¯, hc λkln 1 ` 1 pe λkT ´1 q
(2.4)
defined as the temperature that a blackbody emitting the observed radiation at a particular frequency would have. For downlooking sensors, the brightness temperature can be directly related to the temperature of the observed scene. The definition in Equation 2.4 is not unique; this is the Planck brightness temperature. Other definitions of brightness temperature exist, such as the Rayleigh-Jeans brightness temperature. Brightness temperature can also relate to the total received sensor power (in W) rather than the spectral radiance (in W sr´1 m´2 Hz´1 ), and then there are even more variables in the precise definition. All are expressed in Kelvin, so care is needed when interpreting brightness temperatures.
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Remote sensing
Figure 2.2 also shows what part of terrestrial radiation is transmitted by the atmosphere and what part is not. Radiation emitted by the Sun and then reflected by Earth is referred to as shortwave or solar radiation, whereas radiation emitted by Earth is known as longwave, thermal, or terrestrial radiation. Earth observation satellites measure both. Terrestrial radiation at 8 μm to 13 μm is not significantly absorbed by greenhouse gases and reaches space if no clouds are present. This region of the electromagnetic spectrum is called the window region. Infrared radiation can be either terrestrial, solar, or a mixture of both. A major advantage of measuring terrestrial radiation is that it is available at all times, whereas a measurement of solar radiation requires direct sunlight and is only possible during the day. The work described in this thesis uses only terrestrial radiation. The sensors used are described later. Although negligible energy-wise, microwave radiation as emitted from the Earth’s surface and atmosphere is very valuable for the purposes of remote sensing. More information on passive microwave sensors can be found in section 2.4 on page 15. Note that, depending on context, scientific field and area in the electromagnetic spectrum, different units are used to express the frequency or wavelength of electromagnetic radiation: • Wavelength. Visible and infrared measurements are often referred to by wavelength in micrometres. Wavelength in centimetres may be found in a radar context as well. • Wavenumber. Inverse of wavelength, used in the infrared. Wavenumbers are often given in cm´1 . 8 μm fl 1250 cm´1 and 12 μm fl 833 cm´1 . • Frequency in GHz is used for microwave frequencies. • Others: Energy in eV, not used in atmospheric remote sensing. Radar frequencies are often referred to by band letters (W-band, K-band, etc.) describing frequency regions. The graphic on page 6 illustrates the region of the electromagnetic radiation of interest for this thesis with frequencies in GHz and THz and wavelengths in μm and mm. For a thorough introduction to the physics behind remote sensing, the reader is referred to Rees (2001) or one of the other textbooks on the subject.
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2.2. Sensor considerations
2.2
Sensor considerations
This section discusses some sensor considerations relevant for this thesis. It is not meant to be complete; many aspects, such as polarisation or spectroscopy, are not considered at all, as they are not relevant for this work. Fundamentally, a passive digital remote sensing instrument does not measure spectral radiance or radiant power directly, but some analogue or digital quantity such as noise power or electron count. The spectral response function describes the sensor (channel) sensitivity to different frequencies. The total power received by a sensor, ż8 P “ AΔΩ
f pλqLλ dλ ,
(2.5)
0
relates to the brightness temperature (Rees, 2001, section 6.3.4). In Equation 2.5, P is the power in W, A is area in m2 , Ω is the observed solid angle in sr, λ is wavelength in m, and Lλ is spectral radiance in W sr´1 m´2 Hz´1 . Note that Equation 2.5 is a bit simplified; it assumes that the entire field of view contributes equally to the total sensor observed power. This is not true in general. For example, for microwave sensors, the antenna pattern is not at all constant, and Ω needs to be integrated over as well. Figure 2.3 shows the sensor response functions (SRFs) for Advanced Very-High Resolution Radiometer (AVHRR) channels 4 and 5. The details of sensor technology are beyond the scope of this text.
2.2.1
Imaging
As illustrated with the photograph in Figure 2.1 on page 5, the first remote sensing instruments in space were imagers. An image is a near-instantaneous two-dimensional view of a scene. Imagers are primarily used to determine spatial structures. They do not provide a height resolution and are less well calibrated than sounders. Still, imagers such as AVHRR are used to derive geophysical products. The pixels of a digital image are contiguous, whereas different soundings may be discontiguous. Imagers may have a very high spatial resolution, down to a kilometre or even less. Figure 2.7 illustrates this. Examples of imagers on meteorological spacecraft are AVHRR and Spinning Enhanced Visible Infra-Red Imager (SEVIRI).
10
Remote sensing
NOAA-19 AVHRR SRFs and ARTS-simulated opacity
101
channel 4
channel 5 1
opacity
100
0.8
10´1 0.6 10´2 0.4
10´3
0.2
10´4 10´5 10
Channel response weight
10
2
10.5
11
11.5
12
12.5
0 13
wavelength rμms H2 O N2 O
O3 weights
CO2
Figure 2.3 – Spectral response functions for AVHRR channels 4 and 5 on NOAA-19. Opacities (see Equation 4.4 on page 32) are simulated with ARTS (described in section 4.4). The vertical lines describe an optimised frequency grid as explained in Paper III. This is Figure 1 from Paper III.
2.2.2
Sounding
This section briefly discusses some aspects of atmospheric sounding. For a thorough treatment, please refer to Rodgers (2000). Atmospheric sounding is the measurement of a vertical profile of a some quantity in an atmosphere1 . Commonly measured quantities include temperature, humidity, or the concentration of trace gases. In remote sensing, sounding relies on radiation emitted by the atmosphere. For a down-looking sensor, a height resolution can be obtained by using multiple channels with 1
Sounders such as AMSU and HIRS make a large number of measurements that together can be displayed as an image. However, sounder footprints are not necessarily contiguous, as the distance between soundings may be much larger than the diameter of an individual sounding. It is therefore not correct to speak of images.
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2.2. Sensor considerations
frequencies at different distances from an absorption line. For example, at the water vapour absorption line at 183 GHz, the atmosphere is opaque. Any radiation emitted from the surface is absorbed by the lower atmosphere; therefore, any radiation reaching a satellite sensor must be originating from higher layers in the atmosphere. Channels 18–20 of the AMSU-B instrument are placed at 1, 3, and 7 GHz from the 183 GHz absorption line (see also section 2.4, Figure 2.6, and subsection 4.1.1). The closer to the absorption line, the more absorption, the higher the altitude the radiation is coming from and the colder the brightness temperature. The jacobian is the derivative of the mea- 20 surement vector with respect to the state, y “ Ipxq
J“
dI , dx
Channel 18
(2.6)
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Channel 19 Channel 20
Altitude [ km ]
a matrix that may contain very many rows, because the measurement depends on very many variables. In Equation 2.6, y is the measure- 10 ment vector (such as the three brightness temperatures for AMSU-B channels 18–20), I is the forward model (relating the geophysical state to the measurement, to be described in chapter 4), 5 x is the state (describing everything that can affect the measurement), and J is the jacobian. Figure 2.4 shows three rows of the jacobian 0 for AMSU-B with respect to relative humidity -0.5 -0.4 -0.3 -0.2 -0.1 0.0 Jacobian [ K / 1 ] at different with respect to relative humidity at different altitudes in the US Standard AtmoFigure 2.4 – AMSU-B Jacosphere. Since water vapour concentrations vary bians. in space and time, so does the jacobian. This is Figure 1 from Buehler Sounding only works in the absence of scat- and John (2005). tering. For sounding purposes, scattering is usually undesirable; but scattering can also be signal when it’s information about scatterers — such as (ice) cloud particles — that is to be retrieved. More information about scattering is given in subsection 4.1.2. Unlike the observations by an imager, the observations by a sounder may not be contiguous. For example, the distance between soundings of the latest generation of HIRS instruments is much larger than the field of view of a single sounding. Therefore, in the case of sounders, it is not correct to speak of resolution or pixels, but rather of footprint size and distance between observations.
12
2.2.2.1
Remote sensing
Limb vs. downlooking
The viewing geometry of a sensor is an important design consideration. Most sensors are down-looking. Regardless of whether the sensor can actually see the ground, the observation is directed toward the surface. This may be toward nadir (straight down) or at a particular off-nadir angle, or both for a scanning instrument. A down-looking geometry allows for a good horizontal resolution, but the vertical resolution is poor. An alternate solution is an observation of the limb. By looking at the horizon, a sensor on a satellite platform can observe the atmosphere against a background that is not the Earth: this may be cold space, the Sun, or some other source of radiation. Through scanning, the atmosphere is observed at different altitudes. This allows for a good vertical resolution, but since the radiation path through the atmosphere is long, the horizontal resolution is poor. In this work, only down-looking sensors are used.
2.2.3
Scattering
Radiation interacting with a medium may undergo a scattering process. Scattered radiation changes direction. For a down-looking sensor, the brightness temperature decreases if radiation originating in the lower atmosphere is scattered away from the line of sight. The amount of scattering can be used to obtain information about the total presence of scatterers; for example, to determine the quantity of atmospheric ice. This is the principle for the proposed CloudIce mission by Buehler et al. (submitted 2011). Scattering is further discussed in chapter 4.
2.2.4
Orbits
Two particular orbit types are popular with Earth observation satellites. Almost all Earth observation satellites are either geostationary or Sunsynchronous. The characteristics of those special orbits are described below. Material for this section is drawn from Capderou (2005, sections 4.4 and 4.5). For a geostationary orbit, a) the orbit angular velocity equals the Earth angular velocity, b) the orbit is circular, and c) the orbit lies in the equatorial plane (Capderou, 2005, section 4.4). This results in a satellite that appears stationary for an observer on Earth. This orbit is popular because it allows a continuous observation of the same place. A disadvantage is that it implies a height of 35 788 km above the geoid, so this orbit is not suitable if a high spatial resolution is needed.
2.3. Thermal infrared
13
The plane of a Sun-synchronous orbit is constant with respect to the Sun. Since the Earth is an oblate spheroid, an orbital plane is not constant with respect to the stars, but has a particular precession. If inclination and semi-major axis are chosen such that the precession is exactly one full circle per year, the orbital plane can be constant with respect to the Sun. Apart from technical advantages (such as the lack of a need to rotate solar panels), this offers advantages for Earth observation: the light conditions to observe a particular place are always the same. Sun-synchronous orbits are retrograde with a minimum inclination of 95.7° and a maximum height of 5964 km above the geoid. Sun-synchronous Earth observation satellites are usually in (near-)circular orbits (see also Capderou, 2005, section 4.5). A particular characteristic for a Sun-synchronous orbit is the Local Time Ascending Node (LTAN). Since the orbit is constant with respect to the Sun, the solar time at each ascending (northward) pass over the equator is too2 . Due to perturbations from the gravitational influence of the Sun, the Moon, Jupiter, and irregularities in the Earth geoid, a satellite does not naturally remain in an exact Sun-synchronous orbit. For satellites without an actively controlled orbit, the LTAN drifts over time.
2.3
Thermal infrared
Earth observation sensors operate at wavelengths ranging from 5.6 cm for typical precipitation radars (Karlsson, 1997) to 400 nm to 700 nm for optical imagers, a range spanning five orders of magnitude. In this work, only terrestrial radiation and cloud radar are considered. The instruments used in this thesis work are described in subsequent sections. For a comprehensive overview of Earth observation satellites, the reader is referred to the review papers by Smith et al. (1986) and Kidd et al. (2009). In the context of Earth observation from space, thermal or terrestrial radiation is radiation emitted by the Earth surface and atmosphere. As shown in Figure 2.2, this starts at a wavelength of approximately 3 μm. There is no sharp upper limit for infrared radiation. However, above approximately 15 μm, carbon dioxide and water vapour in the Earth atmosphere absorb all radiation emitted from the surface3 and nadir-looking observations have little to offer. At much longer wavelengths, above around 450 μm, observations start to be interesting once again; but this wavelength is more usually expressed with 2
This is not strictly true, because the Earth orbit around the Sun is not a perfect circle. Because the Earth orbit around the Sun is an ellipse, the LTAN varies by several minutes throughout the year even for an unperturbed sun-synchronous orbit. 3 This is responsible for a significant share of the greenhouse effect.
14
Remote sensing
2.3.1
HIRS
Intensity [10−12W/ (Hz*sr*m2]
the corresponding frequency at 664 GHz and considered sub-mm, rather than infrared, radiation (Buehler et al. 2007; Buehler et al. submitted 2011). Information in this paragraph is obtained from the National Space Science Data Center at http://nssdc.gsfc.nasa.gov/nmc and from Cracknell (1997). Observing terrestrial radiation was one of the first applications of Earth observation from space. Already on the second TIROS satellite, an instrument measuring terrestrial radiation was included. Since then, numerous imagers and sounders have been launched on polar-orbiting, geostationary, and other satellites. The first sounders were launched on the Nimbus-3 satellite in 1969 (Rodgers, 2000) and HIRS was first put in orbit on-board Nimbus-6 on 12 June 1975. Subsequent editions of HIRS were flown on TIROS-N, NOAA-6 and all later NOAA polar orbiting satellites to date. Operational imaging dates back to the launch of the Very High Resolution Radiometer (VHRR) on-board NOAA-2 on 15 October 1972. VHRR was succeeded by AVHRR with the launch of TIROS-N on 13 October 1978. Since then, also AVHRR has been present on all operational polar-orbiting satellites by NOAA. The NOAA KLM User’s Guide HIRS Thermal Radiation Channels 5.5 contains detailed technical informa10 5 tion about the operational meteoro8 5 3 7 4.5 24 6 logical sensors on the NOAA satel1 4 9 lites (Robel et al., 2009). Most of the 3.5 3 information in the paragraphs below ← 299.71K 11 2.5 is retrieved from this User’s Guide. 2
225K→
12
1.5 1 0.5
0 The High resolution Infrared Radia0 500 1000 1500 Wavenumber [cm−1] tion Sounder (HIRS) is a sounder with 20 channels in the visible Figure 2.5 – Positions for HIRS thermal (1 channel), near infrared (7 chan- radiation channels. The black lines show nels), and thermal infrared (12 chan- blackbody curves at various temperatures, nels). The thermal channels are and the blue line shows atmospheric opacshown to the side in Figure 2.5. ity (defined in Equation 4.4). WavenumHIRS obtains 56 Earth view samples ber is the inverse of wavelength, so a at a maximum scan angle of 49.5°, wavenumber of 1000 cm´1 corresponds to corresponding to a swath width of a wavelength of 10 μm. 2179 km. The distance between This is Figure 1 from Buehler et al. (2010). neighbouring samples is 39 km. HIRS/3 (on NOAA-15, -16 and -17) has a footprint diameter at nadir of 20 km, with 19 km to the next footprint. At HIRS/4, the diameter reduced to 10 km, so that the gap between neighbouring footprints increases to 29 km. This is illustrated in Figure 2.7.
2.4. Passive microwave
2.3.2
15
AVHRR
The Advanced Very-High Resolution Radiometer (AVHRR) is an imager with 6 channels (5 are in operation simultaneously) in the visible and infrared. As briefly discussed before, AVHRR has a long history, dating back to 1978 or even 1972. The latest generation, AVHRR/3, flies on NOAA-15–19 and on MetOp-A, all Sun-synchronous satellites. Channels 1, 2, and 3A measure in the visible and near-infrared range and are calibrated in terms of albedo. Channels 4 and 5 measure terrestrial radiation. The spectral response functions of those channels are shown in Figure 2.3. Channel 3B is located in a spectral region where both reflected solar radiation and emitted terrestrial radiation are significant. A single AVHRR scanline consists of 2048 contiguous pixels ranging from 1.1 ˆ 1.1 km2 at nadir to 6.24 ˆ 2.3 km2 at the scan edge. Due to storage and bandwidth limitations, not all data are downlinked globally. Full Resolution Area Coverage (FRAC) data are available only for MetOp-A. For other satellites, full-resolution data are available only for particular regions of the world, at pre-order, or by direct downlink for users operating their own ground station. Global data are available only at a reduced resolution in a product known as Global Area Coverage (GAC). In GAC data, four adjacent samples are averaged and only every third scanline is downlinked, thus reducing the data more than tenfold. Figure 2.7 shows the footprints of GAC data.
2.4
Passive microwave
Karlsson (1997) defines the microwave region as 0.1 cm to 10 cm. This corresponds to a frequency range of 3 GHz to 300 GHz. Spaceborne microwave observations of the atmosphere began with the launch of Nimbus-5 on 11 December 1972, carrying the single-channel Electrically Scanning Microwave Radiometer (ESMR) (Gurney et al., 1993, page 371). Since then, microwave radiometers have gradually improved. The 4-channel Microwave Sounding Unit (MSU) was first launched on TIROS-N on 13 October 1978. MSU has channels from 50.3 GHz to 57.95 GHz and a footprint at nadir with a diameter of 124 km. Nine copies were launched between TIROS-N up to and including the launch of NOAA-14 on 30 December 1994. The similar Special Sensor Microwave/Temperature (SSM/T)-1 has seven channels from 50.5 GHz to 59.4 GHz and a footprint at nadir with a diameter of 174 km. SSM/T-1 is part of the payload of several satellites from the Defense Meteorological Satellite Programme (DMSP) series. Both MSU and SSM/T-1 were temperature sounders. Special Sensor Microwave/Imager
16
Remote sensing
(SSM/I), first launched on 20 June 1987 on DMSP 5D-2/F8, has seven channels from 19.35 GHz to 85.5 GHz and a footprint between 15 km and 69 km depending on frequency. Higher frequency channels became available with SSM/T-2 (from 28 November 1991 on DMSP 5D-2/F11), AMSU (from 13 May 1998 on NOAA-15), and MHS (from 20 May 2005 on NOAA-18), instruments including channels around the strong water vapour absorption line at 183.310 GHz. AMSU-B and MHS are described further below. SSM/T-2 and older sensors are not used in this thesis. Apart from the operational sensors mentioned above, numerous specialpurpose, scientific sensors exist. The reader is referred to the review papers by Kidd et al. (2009) and Thies and Bendix (2011) for more information on recent, current, and future projects.
2.4.1
MHS and AMSU-B
The Advanced Microwave Sounding Unit (AMSU)-B (Saunders et al., 1995) and its successor the Microwave Humidity Sounder (MHS) (Kleespies and Watts, 2007) are microwave radiometers designed for atmospheric sounding of humidity. AMSU-B is carried on NOAA-15, -16, and -17. MHS is carried on NOAA-18, -19, and MetOp-A. Figure 2.6 shows the positions of the channels in AMSU-B. MHS is similar, but channel 2 is at 157 GHz (instead of 150 GHz) and channel 5 has only the band at 190 GHz (instead of 183 ˘ 7 GHz). These bands allow for sounding of atmospheric water vapour, as illustrated in Figure 2.4. From the NOAA KLM User’s Guide (Robel et al., 2009), the antenna spatial response function and the scan characteristics of AMSU-B and MHS are quite similar. Both scan across-track at 90 different viewing angles symmetrically around nadir, with no actual nadir observation. The maximum viewing angle for AMSU-B is 48.95°, for MHS it is 49.44°. For a nominal spacecraft altitude of 833 km, the instantaneous field of view has a diameter of 16 km, corresponding to the half-power level of an assumed Gaussian antenna pattern. This increases to roughly 52 ˆ 27 km2 at the outermost footprint. The effective field of view is slightly larger, because during the integration time, the spacecraft is moving with respect to the Earth surface and the instrument attitude is moving with respect to the spacecraft. Variations in satellite altitude above the surface cause slight changes in the size of the instrument footprint. Figure 2.7 illustrates the effective field of view of MHS.
17
2.5. Radar
1x102
Total Opacity [ ]
1x101
66.5 37.5
1x10
0
10.0 3.0
1x10
-1
1.0 0.5 0.2
1x10-2
1
1x10-3 80
2
100
120
140 160 Frequency [ GHz ]
5 434 5
180
200
Figure 2.6 – Total opacity as a function of frequency for the AMSU-B frequency range. The opacity (see Equation 4.4) is shown for seven different values of Precipitable Water Vapour (PWV). The grey shaded areas show the locations of the AMSU-B channels. Channel positions from the NOAA KLM User’s Guide (Robel et al., 2009). This is Figure 1 from Paper II.
2.5
Radar
A radar is an active instrument. It transmits pulses of radiation at microwave frequencies and measures the backscattered signal as a function of time, thus obtaining information about the distance at which the radiation was backscattered. Radars are widely used for ground-based remote sensing of precipitation (e.g. Karlsson, 1997), but only a small number of atmospheric radars are currently carried on satellites. The first spaceborne radar for atmospheric measurements is part of the Tropical Rainfall Measuring Mission (TRMM), designed to study tropical precipitation. The TRMM radar has an operating frequency of 13.8 GHz (2.17 cm). TRMM data are not used in this study and the mission is only mentioned here for comparison.
18
Remote sensing
2.5.1
CloudSat and the A-Train
The Cloud Profiling Radar (CPR) is carried on-board CloudSat. CloudSat and CPR are described by Stephens et al. (2002); Austin et al. (2009); L’Ecuyer and Jiang (2010), among others. CloudSat is a polar-orbiting, sunsynchronous satellite with an actively maintained LTAN of 13:30. CloudSat was launched 28 April 2006. It is part of the A-Train, or “afternoon train”, a constellation consisting of research satellites dedicated to atmospheric monitoring4 . A recent overview of the A-Train is given by L’Ecuyer and Jiang (2010). Currently (late 2011), it consists of four satellites: Aura, CloudAerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), CloudSat, and Aqua, although CloudSat has now been switched off. The nearly equal orbital tracks between the A-Train satellites allow for numerous synergies. CloudSat and CALIPSO are only 12.5 seconds or 93.8 km apart. The CloudSat radar and the CALIPSO lidar coincide for more than 90% of the time (L’Ecuyer and Jiang, 2010). NOAA-18 and NOAA-19 are sufficiently close to the A-Train to have a large number of collocations, as shown for NOAA-18 in Paper I (NOAA-19 was not launched at the time the work for Paper I was performed). Instruments carried on NOAA-18 and NOAA-19 are described in section 2.3 and section 2.4. Collocations are described in section 2.6. At the time of writing (late 2011), CloudSat is switched off and might not be turned on anymore. If it is still turned on, it will be only during the sunlit part of the orbit and the orbit might be changed to be closer to the terminator, thus outside of the A-Train (from the CloudSat Data Processing Center).
2.6
Collocations
I participated in the third International Workshop on Space-based Snowfall Measurement (IWSSM), organised in Grainau, Germany from 30 March to 2 April 2011. At this workshop, the “Global and Regional Detection and Estimation” working group recommended: Matchups of spaceborne [passive microwave] observations with CloudSat and ground-based radar networks and radar/lidar profiling stations are critical for improving the global snowfall detection capabilities of passive instruments. Radar reflectivity, polarisation, 4 According to L’Ecuyer and Jiang (2010), Aura project scientist Mark Schoeberl coined the name A-Train after a jazz song written by Billy Strayhorn and Duke Ellington.
19
2.6. Collocations Illustration of sensor footprints over the Kiruna region
HIRS/4 MHS AVHRR/3 GAC CloudSat
Kiruna
0
10
20
30
40
50 km
Figure 2.7 – Illustration of footprint sizes for CloudSat, MHS, AMSU-A, and HIRS and pixel size for AVHRR. The data for the background map are OpenStreetMap contributors. C
and in situ datasets should all be considered where available. (IWSSM-3 recommendation) Matchups of spaceborne passive microwave observations with CloudSat — that is exactly what my first paper, Paper I, is about. In the previous section, the sensors used in thesis work were described. Those sensors have been around for a long time and are in constant use both
20
Remote sensing
operationally and scientifically. However, the combination of multiple sensors, or different copies of the same sensor, remains underutilised. This section describes such co-incident measurements. It is more specific than the previous section. Therefore, it contains more references to appended papers. Collocations form the basis of the research in this thesis and are used in Paper I, Paper II, by John et al. (2011a), and in work still to be published. A review of prior research using collocations is given in Paper I.
2.6.1
Criteria
A collocation occurs if different instruments observe the same place at approximately the same time. In the context of this thesis, those instruments are spaceborne remote sensing instruments, usually on different satellites. However, a collocation can also be considered between a satellite-based and a ground-based measurement. Figure 2.7 illustrates the sizes of footprints and pixels for various instruments. The interpretation of “the same place” and “the same time” depends on the instruments and the usage of the collocations. For example, Seiz et al. (2007) match visible imagery on adjacent geostationary satellites to retrieve cloud top height by stereophotogrammetry. For such a high-resolution observation of a rapidly changing environment, the match should ideally occur within a minute. A quite different situation occurs when comparing radiosondemeasured UTH with satellite-retrieved UTH, as done by Moradi et al. (2010). This quantity is changing relatively slowly, and the satellites have a larger field of view. Here, a maximum time interval of two hours is considered acceptable. Such conditions are a tradeoff between the amount of data available and the required precision for the collocation. One can also attempt to correct the location for winds and considered altitude (geolocation data refer to the ground), but this is not done for the present study.
2.6.2
Method
I developed a toolkit to easily find collocations between any pair of sensors. This toolkit has been used to produce several collocated datasets. Over the years, I invested considerable time and effort to make this toolkit as generic as possible. This has led to a wide variety of applications not foreseen when preparing the first collocated dataset. The first version of the algorithm is described in Paper I. The algorithm was significantly revised shortly after this paper was published, because it was
2.6. Collocations
21
not suitable for new collocated dataset. The revised algorithm is described in Paper II. The code is implemented in MATLAB™ and distributed as part of the Atmlab software package.
2.6.3
Collocated datasets
The first collocated dataset is between CloudSat CPR on one hand and AMSU, MHS, and HIRS on operational meteorological satellites on the other hand. Paper I describes in detail how this dataset was produced and what it can be used for. The algorithm to produce collocations was significantly overhauled for the creation of the second dataset, between different copies of AMSU and MHS. The changes between the first and second version are summarised in Paper II. In this paper, global simultaneous nadir overpasss (SNOs) (collocations with both instruments observing the nadir) from the second dataset are used to characterise the latitudinal dependence of inter-satellite biases. A collocated dataset between AMSU-B and cloud-cleared HIRS was produced for the work by John et al. (2011a). In this case, the sensors are on the same satellite. Further possibilities with collocated datasets are discussed in section 5.2.
22
Remote sensing
Chapter 3 Ice clouds The importance of clouds was already briefly mentioned in section 1.3. In section 1.4, the aims of this thesis project were discussed. One of the aims is to improve quantitative measurements of cloud properties from space. This chapter describes in more detail why (ice) clouds are important and what properties we can use to quantify clouds. Those properties may be related to the Earth’s energy budget, to hydrology, or to parameters required to do radiative transfer simulations (see chapter 4).
3.1
Radiative effects
Clouds reflect solar (shortwave) radiation and absorb terrestrial (longwave) radiation. Reflection of shortwave radiation has a surface cooling effect, whereas absorption and re-emission of longwave radiation has a surface heating effect. The magnitude of the net effect is much smaller than the magnitude of either contribution, so a relatively small error in either shortwave or longwave fluxes can cause a relatively large error in the effect at the surface. The global net effect of clouds on surface temperature, atmospheric temperature, absorbed shortwave radiation, and emitted longwave radiation depends on cloud properties. A thorough review on cloud radiative feedback in the climate system is given by Stephens (2005), and most of the material in this section is drawn from there. The magnitude of the shortwave and longwave fluxes through a cloudy atmosphere depend on many bulk and microphysical parameters. Macroscopic changes in cloud cover, temperature and geographic distribution affect mean global fluxes. Cloud albedo depends on cloud optical depth, which in turn depends on geometric cloud thickness and physical properties such as particle 23
24
Ice clouds
sizes, total water or ice content, particle shapes (for ice clouds), and others. An increase in global-mean temperature may change the total shortwave and longwave fluxes and therefore the energy budget of the Earth. The effect of climate change on the sign of the energy budget is not clear. Quoting Stephens (2005): “we have no clear theory that suggests the accumulated effects of cloud feedbacks are in any way a function of global-mean temperature”. Already without considering clouds, at most low latitudes, the net radiation budget is positive: the total power of solar radiation absorbed exceeds the total power of terrestrial radiation emitted to space. At high latitudes, this net budget is negative (Peixoto and Oort, 1992, section 6.8.2). Clouds transmit part of incoming solar radiation, but absorb most terrestrial radiation. At low latitudes, the net effect of clouds is surface cooling, atmospheric heating and a more positive net radiation budget. At high latitudes, the net effect is surface heating and atmospheric cooling (Allan, 2011) and a more negative radiation budget. Thus, clouds enhance the meridional gradient of the net radiation budget and, consequently, atmospheric circulation (Stephens, 2005). High clouds warm the atmosphere by absorbing terrestrial radiation and cool the surface by reflecting solar radiation. In clear-sky conditions, window region radiation reaching space originates from the surface, which can cool down significantly. In the presence of low clouds, this radiation is emitted by the top of the cloud, while surface-emitted radiation is absorbed and radiated back to the surface. Hence, the presence of low clouds leads to the surface being cooled less and the atmosphere being cooled more, compared to a clear-sky situation. This is particularly true at high latitudes (Stephens, 2005). Both cloud optical thickness τ and effective radius re have direct importance for cloud radiative feedback in the climate system. Optical thickness τ affects cloud reflectivity for solar radiation, as described by Nakajima and King (1990). Cloud particle effective radius re affects cloud emissivity for terrestrial radiation for thin clouds. Water, snow, and ice all have an emissivity at 8 μm to 12 μm of more than 0.98 (Rees, 2001, Figure 3.25). Hence, the emissivity of a non-transparent cloud at those wavelengths is also close to one. However, for thin clouds, this emissivity is less than one, and terrestrial radiation may be transmitted. This can be exploited for remote sensing purposes. For example, Rädel et al. (2003) describe the dependence of cloud emissivities at 8 μm and 11 μm on particle effective radius re . In conclusion, both τ and re have direct importance for cloud radiative feedback in the climate system.
3.2. Microphysical properties
3.2
25
Microphysical properties
Figure 3.1 – Examples of ice shapes observed during several flight campaigns. Figure from Heymsfield et al. (2002).
Cloud microphysical properties are important for understanding cloud radiative properties, cloud optical properties, and cloud hydrology. Cloud microphysics is discussed in detail by e.g. Rogers and Yau (1976). Here, only a few cloud properties relevant for this thesis will be discussed. Hydrometeors are atmospheric particles consisting of condensed water, such as cloud droplets, raindrops, or snowflakes. Hydrometeors can be liquid or frozen and come in sizes ranging from particles smaller than a few micrometer to several hundred micrometer (Wallace and Hobbs, 2006), or even larger in the case of snowflakes or hailstones. Additionally, frozen particles come in a large variety of shapes. The shape of a cloud ice particle or of a (precipitating)
26
Ice clouds
snowflake depends on the history of temperature and humidity that the particle went through (Libbrecht, 2005). Figure 3.1 shows examples of ice particles as collected by Heymsfield et al. (2002) during several tropical field campaigns. Often, an ice cloud particle size distribution is required and needs to be assumed. Size distributions are often parametrised based on in situ measurements. The size distribution gives a quantity describing the number of particles (such as particle number or mass density) as a function of the particle size. Since particles may not be spherical, particle size is not uniquely defined. Frequently chosen sizes include the volume equivalent sphere diameter and the maximum diameter. A commonly used size distribution is given by McFarquhar and Heymsfield (1997), henceforth referred to as MH97. MH97 is the sum of a first-order gamma distribution and a log-normal distribution. The distribution depends on Ice Water Content (IWC) and temperature. Particle shapes are (even) harder to parametrise, because there is no single, unique, numerical property to describe the shape. A parametrisation of shapes is still under active development.
3.3
Optical properties
Optical properties describe the interaction of electromagnetic radiation with cloud particles. Note that “optical” does not imply visible radiation, but also applies to other wavelengths, such as infrared or microwave. Optical properties, such as the extinction coefficient, can be measured with reasonable accuracy in a laboratory environment. These optical properties are a function primarily of two microphysical properties: particle size, and particle shape. Optical properties also depend on temperature, because the refractive index does. In the context of this thesis, optical properties are relevant in the context of radiative transfer and their discussion will be deferred to subsection 4.1.2.
3.4
Bulk physical properties
Bulk physical properties are important for the radiative balance and bulk optical properties, but also for hydrological applications and interesting in their own right. Ice Water Content (IWC) is the mass density of ice in an air parcel, commonly expressed in g m´3 . Ice Water Path (IWP) is the IWC integrated along a vertical column,
27
3.4. Bulk physical properties
żzt IWP “
IWCpsqds ,
(3.1)
zb
where s is position along the column and IWP is considered between altitudes zb and zt . Usually, zb and zt span the entire atmosphere. If zb and zt do not span the entire atmosphere, the IWP is a partial-column IWP or pIWP. Cloud Top Height (CTH), Cloud Top Pressure (CTP) and Cloud Top Temperature (CTT) describe the highest physical extent of the cloud. The top of a cloud may not be sharply defined, so some care needs to be taken when considering these quantities. The height (pressure, temperature) of a cloud top is important for understanding measured and simulated radiances from infrared measurements.
28
Ice clouds
Chapter 4 Radiative transfer This chapter contains a brief introduction to those aspects of atmospheric radiative transfer that are relevant for the work described in this thesis. It does not aim to be comprehensive. For a comprehensive introduction, the reader is referred to one of the many textbooks on the subject or to the ARTS Theory Guide, part of the ARTS software distribution described in section 4.4. In the present context, radiative transfer means the simulation of satellite observations as described in chapter 2. All radiative transfer described in this thesis can be simulated using ARTS, a radiative transfer model described in section 4.4. However, ARTS can perform simulations of many additional processes not described in this chapter. In this chapter, radiative transfer is considered for terrestrial radiation only. Solar radiation is not considered. Processes described and assumptions made are mostly valid from approximately 5 μm up to approximately 100 mm or 3 GHz (see also the graphic on page 6).
4.1
Theory
Radiative transfer is most concisely summarised by the radiative transfer equation. Assuming local thermodynamic equilibrium and fully elastic scattering, the radiative transfer equation can be formulated as dIpν, r, n ˆq “ ´βe pν, r, n ˆ qIpν, r, n ˆ q ` βa pν, r, n ˆ qBpν, T prqq ds ż ` Zpν, r, n ˆ, n ˆ 1 qIpν, r, n ˆ 1 qdˆ n1 , 4π
29
(4.1)
30
Radiative transfer
where I refers to spectral radiance in e.g. W sr´1 m´2 Hz´1 . s is the position along the line of sight (in units of length), βe is the extinction coefficient, βa is the absorption coefficient, and Z is the scattering phase function. The absorption coefficient (in m´1 ) is the absorption cross-section per unit volume. The absorption cross-section (in m2 ) for a particle or molecule describes how much radiation is absorbed; all incident radiation passing through this surface is absorbed, all other radiation is not. The scattering coefficient and scattering cross-section are defined similarly, but relate to scattering. The extinction coefficient and extinction cross-section are the sum of the respective absorption and scattering quantities. See also Figure 4.1. The scattering phase function gives the distribution of radiation after a beam is scattered, or, equivalently, the probability density function for a single scattering event. It may be normalised to either the scattering coefficient, the scattering cross-section, or the scattering efficiency (explained later). In Equation 4.1, the scattering ş phase function is normalised with respect to the scattering coefficient, e.g. 4π ZdΩ “ βs . The variables in Equation 4.1 are ν for the frequency in Hz, r for the position in a medium (in our case, an atmosphere), n ˆ and n ˆ 1 are unit vectors for outgoing and incoming radiation, respectively. Finally, T is the local temperature. Equation 4.1 is the scalar radiative transfer equation, where scalar means polarisation effects are not considered. Equation 4.1 describes the change of radiation along the line of sight. Three terms contribute to this change: ˆ qIpν, r, n ˆ q, is preceded by a negative sign and • The first term, βe pν, r, n describes losses through extinction. Radiation losses can occur either through absorption or by the radiation being scattered away from the line of sight. The extinction coefficient βe equals the absorption coefficient βa plus the scattering coefficient βs . ˆ qBpν, T prqq, is the emission source. Kirch• The second term, βa pν, r, n hoff’s law states that absorptivity α equals emissivity . If this were not the case, an object could reach infinite temperature by systematically absorbing more energy than it emits. Similarly, emission in the radiative transfer equation can be equivalently given by the absorption coefficient βa . B is the blackbody radiation as given by Equation 2.1. • The third term,
ş
Zpν, r, n ˆ, n ˆ 1 qIpν, r, n ˆ 1 qdˆ n1 , is the scattering source
4π
term. It describes radiation originating from any direction scattered into the line of sight.
31
4.1. Theory
The primary task of a radiative transfer model, such as ARTS described in section 4.4, is to solve Equation 4.1. particles
molecules
refractive index n
quantum mechanics
Mie/DDA/. . .
calculations, measurements, modelling
absorption efficiency Qa scattering efficiency Qs extinction efficiency Qe
AQ scattering phase function Z
spectroscopic database
bulk
line-by-line code
absorption cross-section σa scattering cross-section σs extinction cross-section σe ř nx σx x
absorption coefficient βa scattering coefficient βs extinction coefficient βe radiative transfer opacity/optical depth τ ...
Figure 4.1 – Summary of optical properties for particles, molecules, as well as the bulk medium. The scattering phase function can be either a single particle property, or a bulk property if averaged over all particles. In the figure, A is the cross-sectional area of a particle.
Figure 4.1 illustrates the relation between various properties occurring in radiative transfer. Those properties are further discussed below.
4.1.1
Clear-sky radiative transfer
In the context of this chapter, “clear-sky” radiative transfer means radiative transfer in the absence of scattering, whereas “cloudy” radiative transfer means radiative transfer with scattering particles. In reality, gases and aerosols also scatter radiation. In this thesis, aerosols are not considered, and for terrestrial radiation (λ ą 5 μm), scattering from gases can be neglected. Physical processes important in clear-sky radiative transfer are still important in cloudy radiative transfer and the solution for clear-sky radiative transfer can be considered as a subset of the solution for cloudy radiative transfer.
32
Radiative transfer
However, the solution approach is different, because the cloudy problem is considerably more complex (more factors are involved) and more complicated (a more difficult problem to solve). In the wavelength under consideration here, the only relevant processes for clear-sky radiative transfer are absorption and emission, so that dIpν, r, n ˆq “ βa pν, r, n ˆ q rBpν, T prqq ´ Ipν, r, n ˆ qs , ds
(4.2)
which is Equation 4.1 with βe “ βa and Z “ 0. Equation 4.2 can be solved analytically. If emission can be neglected (i.e., because there is a very strong source), it becomes the Lambert-Beer law, I “ I0 e´τ , where τ is the optical depth or the opacity, żl τ ” βa dl1 ,
(4.3)
(4.4)
0
as illustrated in Figure 4.1. As illustrated in Figure 4.1, the determination of βa starts with fundamental quantum-mechanical considerations. Electromagnetic radiation interacts with the various gases present in the atmosphere. Each constituent gas absorbs at particular regions in the electromagnetic spectrum. From quantum-mechanical considerations, multi-atom molecules (as almost all gases constituting the atmosphere are) can vibrate and rotate according to discrete states. Only photons with an energy equal to the difference between a currently held energy level and a higher energy level can be absorbed. Those frequencies correspond to absorption lines. Equivalently, higher energy levels are reached due to thermal excitation, and photons with corresponding frequencies are emitted by anything with non-zero temperature. From just considering the transitions, absorption lines would have no width and absorption would occur only if the photon frequency exactly matches the transition frequency. However, several processes cause so-called line broadening. Due to the Heisenberg uncertainty principle, the frequency associated with an absorption line is not exactly determined, but has a certain a) natural broadening. Molecules do not exist alone, but are part of an ensemble of many molecules forming a gas, a liquid, or a solid. Consequently, nonzero temperature and pressure cause b) thermal and c) pressure broadening, respectively. Natural broadening is very small compared to thermal and pressure broadening, and in the troposphere, pressure broadening is the dominating mechanism.
4.1. Theory
33
For the absorption coefficient βa , all lines for all constituent gases need to be considered. Those lines and their dependences are catalogued in databases such as the HIgh resolution TRANsmission (HITRAN) database (Rothman et al., 2009). More information on gaseous absorption can be found in textbooks such as Goody and Yung (1995), Liou (2002), or in the ARTS Theory Guide (Eriksson et al., 2011b) and references therein.
4.1.2
Particles
Like molecules, particles emit and absorb electromagnetic radiation. Unlike molecules at infrared and microwave wavelengths, particles additionally scatter incoming radiation. For remote sensing of clouds, scattering, absorption, and emission by clouds can all be relevant, depending on cloud phase, particle size, and wavelength. In the context of this thesis, only elastic scattering (where the frequency does not change) is relevant. The physics of scattering by particles is an entire field in itself. This thesis only scratches the surface. For details, the reader is referred to textbooks such as the ones by Mishchenko et al. (2002) or Liou (2002), or to the ARTS Theory Guide (Eriksson et al., 2011b) and references therein. Material in this section is drawn from these sources and from Wallace and Hobbs (2006, subsection 4.4.1). In clear-sky radiative transfer, the absorption coefficient βa can (in theory) ultimately be determined from quantum-mechanical considerations along with knowledge of the atmosphere, as described above and illustrated in Figure 4.1. For radiative transfer in a cloudy atmosphere, those considerations are not sufficient for the determination of βa and the determination of βa is not sufficient to solve the radiative transfer equation. To solve Equation 4.1, additionally the extinction coefficient and the scattering phase function are needed. The extinction coefficient describes the total amount of scattering in a volume, whereas the bulk scattering phase function (as mentioned before) describes the distribution of radiation after a beam of radiation is scattered (or, equivalently, the probability density function for a single scattering event). As illustrated in Figure 4.1, those properties can be obtained starting from the fundamental material properties for the scattering object (typically water or ice). Interaction between radiation and particles is a function of refractive index (which in turn is a function of temperature), size in relation to wavelength, and of particle shape. As a first consideration, the order of magnitude of the
34
Radiative transfer
ratio between particle size and wavelength, also known as the size parameter, r x9 , λ
(4.5)
can tell us what kind of interaction we might expect. Here, r is a characteristic particle size, which may be the radius for a spherical particle or the volume equivalent radius for a non-spherical particle. The exact value of x is not important, but the order of magnitude is. The wavelengths of electromagnetic radiation considered in this thesis vary by four orders of magnitude (see page 6) and so do the sizes of atmospheric ice particles (see section 3.2). Since those are independent, the size parameters x can vary over a range of 7 to 8 orders of magnitude (see Table 4.1). Size parameter x “ Type Snowflake Raindrop Ice crystal Cloud droplet
Characteristic 10 μm length (mm) 10.0 1.0 0.1 0.01
6 ˆ 102 6 ˆ 101 6 6 ˆ 10´1
2πr λ
1.6 mm fl 183 GHz 4 ˆ 101 4 4 ˆ 10´1 4 ˆ 10´2
Table 4.1 – Size parameters for typically occurring hydrometeors in the atmosphere, observed at infrared and microwave wavelengths. Based on Liou (2002, Table 5.1).
Different models exist to calculate particle optical properties (summarised in Figure 4.1) in either exact or approximate ways. Many of those models are described in Mishchenko et al. (2002) and in Mishchenko et al. (2000). As illustrated in the top-left panel of Figure 4.1, such models take as an input the refractive index n and particle physical properties, and generate as an output the scattering phase function and two parameters uniquely characterising the absorption efficiency, scattering efficiency, and the extinction efficiency. The scattering efficiency is defined as the ratio between the scattering cross-section and the geometric cross-section. The absorption efficiency and extinction efficiency are defined in an analogous way. For spherical particles, Lorenz-Mie theory describes exactly and analytically the interaction between electromagnetic radiation and scattering particles, by expressing the scattering efficiency and the scattering phase function in terms of refractive index and size parameter. A derivation can be found in Liou (2002, section 5.2).
35
4.1. Theory
When x ! 1, the Rayleigh scattering approximation applies and the scattering efficiency follows Qs 9 λ´4 . In the Rayleigh regime, scattering is weak and gets weaker rapidly with wavelength. Rayleigh scattering is important for visible light scattering from molecules and causes the blueness of the sky, because blue light (which has a long wavelength) undergoes (multiple) scattering and arrives at the observer from all directions, whereas yellow light (which has a short wavelength) arrives mainly straight from the Sun. Rayleigh scattering also occurs for microwave scattering from small cloud particles, but the number density of cloud particles is too small for this to be of any significance for passive remote sensing purposes. The Rayleigh approximation is also valid for non-spherical scatterers. Rayleigh scattering phase functions are quite smooth, like the one shown in panel (b) in Figure 4.2. For scattering from atmospheric ice particles, x ! 1, Qs 9 λ´4 , and the Rayleigh approximation is no longer valid. In this regime, the shape of the scattering particle is important. For non-spherical particles, Lorenz-Mie theory does not apply and no analytical solution exists (Liou, 2002, section 5.4). The T-Matrix method is applicable to rotationally-symmetric particles. Generic methods that can be applied to particles of arbitrary shape are computationally expensive. Mishchenko et al. (2000) provide an overview of numerical methods and laboratory measurements to determine optical properties of particles of arbitrary shape. Such methods include, but are not limited to, Discrete Dipole Approximation (DDA) and Finite Difference Time Domain (FDTD). Table 4.2 Shape
Method
Spherical Lorenz-Mie Rotationally symmetric T-Matrix Other DDA, FDTD, . . .
Remark exact
Table 4.2 – Summary of scattering calculation methods for ice particles. References e.g. Mishchenko et al. (2000).
summarises various methods. For both spherical and non-spherical particles, when x ! 1, the scattering efficiency does not strongly depend on wavelength as it does in the Rayleigh regime (for spherical non-absorbing particles Qs pxq oscillates and lim Qs “ 2). xÑ8 In a cloud, all incident light undergoes multiple scattering. Additionally, many different sizes are represented in a typical cloud. Through the entire cloud, all incident light undergoes roughly the same scattering process. This is why clouds generally appear white, as only in a cloudy sky the Sun reveals its true white colour.
36
Radiative transfer
ˆ10´14 λ = 5.3 μm k = 1887 cm´1 r = 49 μm
10´8 10´9 10
´10
10
´11
λ = 0.9 mm ν = 333 GHz r = 40 μm
1.6 “ ‰ P pθq m2
“ ‰ P pθq m2
10´7
1.4 1.2 1 0.8
0
45
90 θ r°s
(a) Infrared
135
180
0
45
90
135
180
θ r°s (b) Microwave/sub-mm
Figure 4.2 – Illustration of typical scattering phase function for infrared ((a), from Yang et al. (2005)) and microwave ((b), from Hong (2007)). Note that part (a) has a logarithmic y-scale.
Figure 4.2 shows two scattering phase functions, here normalised to the μm scattering cross-section in m2 . In Figure 4.2a, x “ 2π49 “ 58, and in 5.3 μm 2π40 μm Figure 4.2b, x “ 0.9 mm “ 0.28, so neither scattering phase function is in the Rayleigh regime, although the microwave one is quite close. Several differences are apparent from the figure: • The scattering cross-section in the infrared example is much larger than the one for the microwave example, as can be seen by looking at the values printed at the y-axis. This makes intuitive sense, because the particle is so much larger relative to the wavelength, as quantified by the size parameter. Indeed, thin clouds consisting of small particles are transparent at microwave frequencies, whereas a cloud does not need to be very thick for it to be opaque at infrared wavelengths. • The scattering phase function for the infrared example has a very strong forward peak, whereas the scattering phase function in the microwave example is very smooth. Solution methods that discretise the scattering phase function, such as the Discrete Ordinate ITerative (DOIT) method, would need a very fine angular grid to fully characterise the forward peak. A very fine angular grid is computationally expensive. Therefore, methods that do not discretise the scattering phase function, such as Monte Carlo (MC) methods, are advantageous. Both DOIT and MC are briefly discussed in subsection 4.4.2.
4.2. Practical considerations
37
• The scattering phase function for the infrared exhibits an oscillatory behaviour as a function of the scattering angle. Like the strong forward peak, an accurate characterisation of these oscillations with discrete ordinate methods like DOIT requires a very fine angular grid. Again, MC methods do not suffer from this problem. Although Figure 4.2 is for illustration purposes only, the conclusions can be generalised for other shapes. The shape of the scattering phase function depends mainly on the size parameter, and to a lesser degree on the particle shape.
4.2 4.2.1
Practical considerations Sensors
All prior considerations in this chapter consider monochromatic pencil beam simulations without considering either the spectral response function or the antenna pattern. The observed channel radiance is given by Equation 2.5 (page 9). To simulate Equation 2.5, a number of monochromatic pencil beam simulations need to be carried out in order to characterise the total channel power. The naive way to carry this out would be to use a grid for both the frequency grid and the sensor field of view. However, this might result in very many radiative transfer calculations, which can be very expensive, particularly for cloudy simulations. Fortunately, other methods exist; see, for example, subsection 4.4.1 for a method, implemented in ARTS, to significantly reduce the number of monochromatic pencil beam calculations.
4.2.2
Databases
Calculation of optical properties are expensive, in particular for non-spherical particles. Precalculating optical properties and storing them in a lookup table can save considerable calculation time later on. If optical properties are stored for many frequencies and sizes, memory consumption may be huge. However, if optical properties are stored only for a small number of frequencies and sizes, significant errors may be introduced due to interpolation. Examples of commonly used databases for single scattering properties are the ones by Hong et al. (2009) for microwave radiances and by Yang et al. (2005) for infrared radiances. The scattering phase functions shown in Figure 4.2 are from these sources.
38
4.2.3
Radiative transfer
Sources for profiles
To perform radiative transfer simulations, atmospheric data is required. Those can be obtained from different sources, such as a) remote sensing measurements, b) in situ measurements, or c) output from general circulation models (GCMs) . Method (b) is often limited to clear-sky data. In this thesis work, profiles originate from atmospheric models. Chevallier et al. (2006) have selected 25 000 profiles from European Centre for Medium-range Weather Forecasting (ECMWF) Re-Analysis (ERA)-40 model data. The profiles were selected to maximise variability in five different quantities: a) temperature, b) relative humidity, c) ozone mixing ratio, d) cloud condensate, and e) precipitation. This dataset is suitable for developing empirical retrievals, because it aims to span the full variability of atmospheric states (at least those occurring in ERA-40) with a limited number of profiles. This is the dataset used in Paper III. This dataset is not suitable for studying statistical relationships, because the distribution of atmospheric parameters is very different from the natural one. However, to get the full span of atmospheric states from a random selection of model output, the number of profiles required is too large to be feasible for radiative transfer studies. In this case, a compromise between the two needs to be made.
4.3
Retrieval development
In the context of remote sensing, a retrieval is the process of obtaining geophysical properties (such as IWP) from the direct, calibrated measurement, such as an instrument radiances or radar backscatter. For a review on existing retrievals of cloud properties, please refer to Stephens and Kummerow (2007). The theses by Eliasson (2011) and Rydberg (2010) contain additional discussion and further references. One way to develop a retrieval is by training an ANN or a similar regression method with a retrieval database. A retrieval database is a table of radiances (as measured by the instrument) and geophysical parameters (the final quantity of interest). Paper I describes how to obtain a retrieval database from collocations and then use this database with an ANN to train a retrieval. Alternatively, radiative transfer simulations may be used to obtain a retrieval database. Regardless of the origin of the retrieval database (measurements or simulations), it is important that the statistics of the input atmospheric data span the entire range of possible atmospheric states to be retrieved. Depending on
4.4. ARTS
39
the regression method used for the retrieval, it may also be important that statistics are well-represented. Synergies between retrieval databases from collocations and retrieval databases from radiative transfer simulations will be explored in the future.
4.4
ARTS
The Atmospheric Radiative Transfer Simulator (ARTS) is a radiative transfer model for the simulation of radiative transfer of terrestrial radiation. ARTS can calculate polarised radiances in up to three dimensions in any geometry above a planet of arbitrary shape. It can obtain either (monochromatic) pencil-beam spectral radiances or calculate passive instrument radiances, taking into account the spectral response function and the antenna pattern. An overview of the capabilities of ARTS is given by Eriksson et al. (2011a), with more details in the references therein and in the ARTS User Guide (Eriksson et al., 2011c). ARTS is the sole radiative transfer model used in this thesis work.
4.4.1
Optimisations
ARTS is a physical model in the sense that it solves the radiative transfer equation starting from first principles as illustrated in Figure 4.1. This makes ARTS slow compared to many other models that might use parametrisations for the characterisation of clouds. However, ARTS implements a number of optimisations to make simulations faster, without compromising much on accuracy. A full characterisation of gaseous absorption for a typical channel on an infrared radiometer (Figure 2.3, page 10) requires a much larger number of monochromatic pencil beam simulations than a full characterisation of a channel radiance on a microwave radiometer (Figure 2.6, page 17). To fully resolve all absorption lines on an infrared radiometer, thousands of monochromatic pencil beam simulations need to be simulated. Buehler et al. (2010) describe a method to derive a small set number of frequencies that are representative for the entire channel, even without resolving all absorption lines. For HIRS, Buehler et al. (2010) show that a relative error in channel radiance of less than 10´4 can be obtained by simulating spectral radiances for less than twenty frequencies. Buehler et al. (2010) apply this to clear-sky simulations, but in Paper III we show that this is also applicable to cloudy simulations.
40
Radiative transfer
Other optimisations implemented in ARTS are an absorption lookup tables (Buehler et al., 2011) and a sensor response matrix (Eriksson et al., 2006).
4.4.2
Scattering
In a radiative transfer simulation, ARTS treats the clear-sky and the cloudy parts separately. For the cloudy part, two different solvers exist: • The DOIT method is a polarised three-dimensional discrete ordinate solver for cloudy radiative transfer. It was developed by Emde et al. (2004), primarily for microwave and sub-mm radiances. DOIT relies on a discretisation of the scattering field. This causes a problem for strongly non-linear scattering phase functions as occur for typical ice crystals in the infrared (see Figure 4.2), because it would require a very fine angular grid to fully resolve the scattering phase function and calculations would become very slow. Although methods exist to alleviate this (e.g. Wiscombe, 1977), those have not been implemented in ARTS. • In the context of radiative transfer, the MC approach involves simulating the radiative transfer statistically. A general overview is given by Mayer (2009). The implementation of MC in ARTS is described by Davis et al. (2005). ARTS implements a reverse MC approach, which means photons are “generated” at the sensor and then traced backward. The photon is transmitted through the three-dimensional model atmosphere step by step. At each step, local optical properties determine the chance that the photon was emitted or scattered at this point. If it is scattered, a random direction is drawn according to the scattering phase function. Therefore, the performance of a MC algorithm does not suffer from a strongly peaked scattering phase function1 . For this reason, ARTS-MC is the tool of choice in this thesis work.
1
This is not strictly true, because ARTS-MC employs rejection sampling. In rejection sampling, a random number is drawn and then accepted with a probability defined by the value of the probability distribution function at the drawn number. An alternative method would be inverse transform sampling, which calculates the value of the cumulative distribution function at the point of a uniformly randomly drawn number between 0 and 1. Whether this would speed up ARTS-MC might be worth investigating in the future.
Chapter 5 This thesis
5.1 5.1.1
Paper summaries Paper I G. Holl, S. A. Buehler, B. Rydberg, and C. Jiménez. Collocating satellite-based radar and radiometer measurements – methodology and usage examples. Atmos. Meas. Tech., 3: 693–708, 2010. doi: 10.5194/amt-3-693-2010 Included at page 63.
Paper I describes collocations between CloudSat Cloud Profiling Radar and NOAA-18 MHS. The paper is based on the work I did for my Master Thesis (Holl, 2009). It consists of three parts. Firstly, the paper describes an algorithm to find collocations. This algorithm is optimised for collocations between two instruments where at least one instrument observes at a fixed viewing angle (typically the nadir), so that observations lie on a line. All footprints are treated as point measurements, and collocations depend only on distance in space and time between different footprints. Collocation criteria are split in a spatial and temporal part. If there is any temporal overlap (˘ the time criterion) between two considered granules (a granule being one file containing satellite data, typically one orbit), the spatial criterion is tested. This is done based on the assumption that the distance between footprint n and footprint n ` 1 is smaller than the distance between footprint n ` 1 and footprint n ` 2. N equidistant points are selected from ground track A and the distances to footprint p from ground 41
42
This thesis
track B are calculated. If any of those distances meet the spatial criterion, the distances to all footprints in the vicinity of those footprints are calculated. If no distances meet the this criterion, the procedure is repeated with another footprint from ground track B. The algorithm is explained in full detail in Paper I. Secondly, Paper I applies the algorithm to find collocations between CloudSat CPR and the suite of AMSU-A, AMSU-B, MHS, and HIRS on the NOAA and MetOp operational meteorological satellites. The paper shows that only NOAA-18 has global collocations with CloudSat CPR1 . It presents patterns in MHS viewing angles and latitudes at which collocations occur, and shows that those collocations do not occur all the time, but intermittently. Since MHS footprints are much larger than CPR footprints, the paper presents two datasets: one dataset presenting all CPR footprints for every collocation, and one dataset presenting statistics for one averaged CPR footprint for every collocation. Those collocations are available for public use. Finally, Paper I explores several applications for the datasets derived in the second part. Three applications are presented. The first application is a direct comparison between MHS-averaged CPR IWP and an IWP product from NOAA National Environment Satellite, Data and Information Service (NESDIS) Microwave Surface and Precipitation Products System (MSPPS). This comparison shows that MSPPS IWP is much smaller than CPR IWP, even for clouds that are visible at MHS frequencies. The second application looks at statistics between brightness temperatures and IWP. The statistics between the two are compared between a dataset with simulated brightness temperatures developed by Rydberg et al. (2009) and a dataset based on collocations. Although small differences exist between the two datasets, the features are largely the same. For the third application, the collocated dataset is used as a training database for the development of an IWP retrieval. A subset of nadir-looking, tropical, MHS-averaged, cloudy collocations is selected. This subset is then used to train an ANN, mapping MHS channels 3–5 against CPR IWP. The resulting network can then be used to retrieve IWP. Paper I then presents the performance of this retrieval and studies how it is affected by adding HIRS channels. Since clouds with IWP smaller than 100 gm´2 are invisible to passive microwave radiation, and clouds with IWP larger than 100 gm´2 are opaque to passive microwave radiation, addition of HIRS should significantly increase the retrieval. However, the effect is small, partly because of the poor horizontal sampling by HIRS. In conclusion, Paper I shows that collocations are a highly useful tool with a large variety of applications. 1
NOAA-19 was not launched at the time this investigation was performed
5.1. Paper summaries
43
I did all work for Paper I, except the description of the dataset developed by Rydberg et al. (2009).
5.1.2
Paper II V. O. John, G. Holl, S. A. Buehler, B. Candy, R. W. Saunders, and D. E. Parker. Understanding inter-satellite biases of microwave humidity sounders using global SNOs. J. Geophys. Res., 2011b. in press Included at page 81.
Paper II uses a newly developed collocated dataset to globally compare nadir observations from different copies of the MHS and AMSU-B sensors on sun-synchronous satellites. It exploits the drift in LTAN (see subsection 2.2.4) for operational satellites from NOAA and MetOp. This drift, illustrated in Figure 3 in Paper II, causes some pairs of satellites to temporarily have the same LTAN. During these periods, collocations between such a pair of satellites occur globally. The algorithm I developed for Paper I is not optimal for the purposes in Paper II, because it considers only the ground track. In Paper I, one of the considered instruments has observations only along the ground track, but for Paper II, both are scanning instruments2 . Therefore, I improved the collocation algorithm. In the new algorithm, all observations from both instruments are gridded in equirectangular bins based on the observation latitude and longitude. Then, distances are calculated between all observations from sensor A in gridbox pi, jq to all observations from sensor B in gridboxes pi ´ n, j ´ mq to pi ` n, j ` mq, where n and m are a function of collocation distance and latitude. Paper II considers only near-nadir collocations, here referred to as SNOs. It presents collocations between NOAA-16 and NOAA-15 during August 2008, between MetOp-A and NOAA-17 during April and May 2009, and between NOAA-19 and NOAA-18 during September 2009. The collocations are then used to explore the latitudinal dependence of inter-satellite biases. The paper shows that the latitudinal dependence is significant, and that an intercalibration of humidity sensors needs to take this into account. My contribution to Paper II was the development and application of this algorithm, and the description in the appendix of Paper II. I developed the 2 Even though Paper II uses only (near)-nadir collocations, I wanted to optimise the collocation algorithm in any case.
44
This thesis
algorithm not exclusively for the purposes of Paper II, but also for other (still unpublished) research.
5.1.3
Paper III G. Holl, S. A. Buehler, J. Mendrok, and A. Kottayil. Simulating cloudy thermal infrared radiances with an optimised frequency grid in the radiative transfer model ARTS. J. Quant. Spectrosc. Radiat. Transfer, to be submitted Included at page 95.
Paper III shifts the focus to radiative transfer. The paper builds on the work by Buehler et al. (2010). Buehler et al. (2010) present a method to derive an optimised frequency grid for the simulation of radiances observed by broadband sensors. Buehler et al. (2010) apply this to the infrared radiometer HIRS and show how the number of frequencies can be reduced from several thousand to less than twenty, but show this only for clear-sky simulations (without scattering). In Paper III, we show that the same frequency grid can be used for simulations of cloudy atmospheres. In the paper, we select 50 profiles from a dataset by Chevallier et al. (2006). For all profiles, we use the ARTS-MC model to perform ten simulations for HIRS channel 11 (7.33 μm) with the reference grid, and ten simulations with the optimised grid from Buehler et al. (2010). Additionally, we apply the method from Buehler et al. (2010) to AVHRR channel 5 (10.8 μm), and perform the same comparison as for HIRS channel 11. In both cases, we show that the magnitude of the bias is less than 0.04 K and the magnitude of the root mean square error is less than 0.4 K. We also investigate the tradeoff between runtime and MC error for different numbers of photons per monochromatic pencil-beam, for both the reference grid and the fast grid. For AVHRR-5, the reference grid contains 5461 frequencies, while the fast grid contains only 5 frequencies. A reference grid simulation with 1 photon per frequency (5461 for the entire channel) has roughly the same accuracy as an optimised grid simulation with 1000 photons per frequency (5000 for the entire channel). However, the simulation with the optimised grid runs much faster, likely due to reduced overhead associated with each monochromatic pencil beam simulation. The results from Paper III will be used for a statistical study of the cloud signal in infrared radiances from simulations and collocations. For Paper III, I have done almost all work and written all text.
5.2. Outlook — Road to PhD
5.2
45
Outlook — Road to PhD
The licentiate thesis describes a work in progress. I have started my PhD in August 2009 and I have approximately two years left until I finish. Many branches extend from the work I have performed so far, and all papers presented call for further work. Paper I presents a comparison between CPR IWP and NOAA NESDIS MSPPS IWP. Eliasson et al. (2011) compare spatial distributions of IWP between different models and measurements, but only based on monthly means. A logical next step would be to combine the work in Paper I with the work by Eliasson et al. (2011) and use collocations for a more in-depth comparison between different IWP products. This project will be mainly carried out by Salomon Eliasson, with a major contribution from me. Paper I shows a new IWP retrieval, but this work is not finished. For example, a cloud screening is completely missing. Paper I attempted to improve the IWP retrieval by adding HIRS radiances, but this did not go so well. AVHRR has a considerably smaller footprint than HIRS, and a much higher spatial resolution. Therefore, it would be worthwhile to obtain a retrieval database from collocations from a combination of AVHRR and microwave radiances, mapped against CPR IWP like in Paper I. Paper I also presents statistics of a mapping of MHS radiances against CPR IWP, compared between collocations and simulated radiances from artificial atmospheres. This work can be built upon and extended to infrared radiances, using output from cloud-resolving models and the radiative transfer configuration described in Paper III. The dataset presented in Paper I could be extended to include full CPR profiles. With such a dataset, CPR measurements could be used to simulate radiances for passive instruments, and those could be compared directly against collocated measurements. The collocation algorithm currently does not consider the actual size and shape of footprints. An improvement could be implemented that takes these factors into account. Paper II use SNOs between different microwave humidity sensors on NOAA and MetOp satellites. The same method can be applied for different sensors in the same satellites, such as HIRS. The work can also be extended to other satellites, such as the satellites in the DMSP programme (see section 2.4), that carry sensors similar to AMSU-B and MHS. The collocated dataset used in Paper II could be extended to include all combinations of angles. Such a dataset could be used to statistically determine the so-called limb cooling: sounding channel jacobians rise for
46
This thesis
off-nadir viewing angles, so the sensor observes a colder region (assuming a tropospheric signal). In Paper III, I use the work from Buehler et al. (2010) and apply it to AVHRR channel 5. This work could be easily extended to AVHRR channel 4, as well as similar channels on SEVIRI, carried on-board geostationary satellites. For the strongly non-linear phase functions as occur for infrared cloudy simulations, it may be worth implementing inverse transform sampling as an alternative to rejection sampling. With the skills I have developed, in particular for radiative transfer modelling, I intend to contribute to work performed by others in our research group. For example, projects are currently going on related to sub-millimetre radiometry and radiative transfer in planetary atmospheres. If possible, I would like to contribute to this where I can. Otherwise, surely the future will bring new opportunities not currently foreseen. After all, the path of science is considerably less predictable than the path of a photon through the Earth’s atmosphere.
References
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Glossary
A-Train “Afternoon Train”, constellation of scientific satellites. Consists of Aqua, CloudSat, CALIPSO (carrying a lidar), and Aura. See also subsection 2.5.1. 18 absorption coefficient (βa ) Quantity describing the amount of absorption per unit length [m´1 ]. See also subsection 4.1.2. 30, 31, 33, 57 absorption cross-section (σa ) The power of monochromatic energy absorbed is the product of incident power and absorption cross-section [m2 ]. See also subsection 4.1.2. 30, 31 absorption efficiency (Qa ) For a particle, the ratio between the geometric cross-section and the absorption cross section. See also subsection 4.1.2. 31, 34 absorptivity (α) Unitless quantity for a layer or surface describing what fraction of radiation passing through the layer is absorbed. 30 Advanced Microwave Sounding Unit 20-channel microwave sounder for temperature (AMSU-A, 15 channels) and humidity (AMSU-B, 5 channels) sounding. See also section 2.4. 59 Advanced Very-High Resolution Radiometer Imager in the visible and thermal infrared. See also section 2.3. 59 Atmospheric Radiative Transfer Simulator Radiative transfer model for the thermal infrared, sub-mm, and microwave. 59 blackbody A blackbody is a body that emits electromagnetic radiation according to Planck’s law, with an emissivity equal to one. See section 2.1. 6 brightness temperature Unit of radiance. See Equation 2.4 on page 7. 7, 9, 11, 12, 42 Cloud Profiling Radar 94 GHz cloud radar carried on-board CloudSat. See also section 2.5. 41, 56, 59 Cloud Top Height Height of the top of a cloud. See section 3.4. 59 55
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Glossary
Cloud Top Pressure Pressure at cloud top height. See section 3.4. 59 Cloud Top Temperature Temperature at cloud top. See section 3.4. 59 CloudSat CloudSat is a satellite dedicated to the study of clouds. It carries the Cloud Profiling Radar. See also subsection 2.5.1. 2, 3, 18, 19, 21, 41, 42, 55 collocation Simultaneous observation of a scene by different remote sensing instruments. See also section 2.6. 3, 4, 18, 20, 21, 38, 39, 41–43, 45 emissivity () Unitless quantity describing how well a surface emits in relation to a blackbody. Equal to absorptivity. 6, 30 extinction coefficient (βe ) Quantity describing the amount of extinction per unit length [m´1 ]. See also subsection 4.1.2. 26, 30, 31, 33 extinction cross-section (σe ) The power of monochromatic energy absorbed or scattered is the product of incident power and extinction crosssection [m2 ]. See also subsection 4.1.2. 30, 31 extinction efficiency (Qe ) For a particle, the ratio between the geometric cross-section and the extinction cross section. See also subsection 4.1.2. 31, 34 geoid Shape of the Earth. This is often approximated by a reference ellipsoid. To a first order of approximation, the Earth can be assumed spherical. To a second order, the Earth is an oblate spheroid. The geoid is the actual shape, whereas the reference ellipsoid is an approximation of this shape. 12, 13 geostationary A satellite in a geostationary orbit appears stationary for an observer on Earth. See also subsection 2.2.4. 12 High resolution Infrared Radiation Sounder Infrared sounder for sounding of temperature and humidity. 59 HIgh resolution TRANsmission Spectroscopic database. See subsection 4.1.1. 60 hydrometeor A hydrometeor is a condensed atmospheric water particle, such as a cloud droplet, a cloud ice particle, a raindrop or a snowflake. 25 Ice Water Content Mass of ice in a unit of air. Usually expressed in g m´3 . 60 Ice Water Path Column density of atmospheric ice. 60 jacobian Derivative of measurement vector with respect to the state vector. See also Equation 2.6. 11, 45
Glossary
57
Local Time Ascending Node For a Sun-synchronous orbit, the local time at which the satellite passes the equator northward. See also subsection 2.2.4. 60 Lorenz-Mie theory Model of interaction between electromagnetic radiation and spherical scatterers. Mostly used when wavelength and diameter have the same order of magnitude and no approximation (such as Rayleigh scattering) can be made. See also subsection 4.1.2. 34, 35 Microwave Humidity Sounder 5-channel microwave radiometer designed for tropospheric sounding of humidity, similar to AMSU-B. See also section 2.4. 60 şl opacity (τ ) τ “ 0 βa dl1 where βa is the absorption coefficient. 10, 14, 17, 31, 32, 57 optical depth see opacity. 31, 32 Planck’s law Planck’s law describes the energy as a function of wavelength emitted by a body at a particular temperature. See section 2.1. 6 radiative transfer Radiative transfer is the modelling of the propagation of electromagnetic radiation. See also chapter 4. 3, 4, 23, 26, 29–33, 37–40, 44–46, 55 retrieval A retrieval in a remote-sensing context is the process of obtaining geophysical parameters from radiance measurements. See also section 4.3. 38 scattering coefficient (βs ) Quantity describing the amount of scattering per unit length [m´1 ]. See also subsection 4.1.2. 30, 31 scattering cross-section (σs ) The power of monochromatic energy scattered away from the line of sight is the product of incident power and scattering cross-section. See also subsection 4.1.2. 30, 31, 34, 36 scattering efficiency (Qs ) For a particle, the ratio between the geometric cross-section and the extinction cross section. See also subsection 4.1.2. 30, 31, 34, 35 scattering phase function (Z) Probability density function describing the directions radiation is most likely to be scattered. See also subsection 4.1.2. 30, 31, 33–37, 40 simultaneous nadir overpass see collocation. 60 spectral radiance (I) Electromagnetic radiation emitted per unit area at a particular wavelength/frequency into a particular solid angle. Often expressed in W sr´1 m´2 Hz´1 . See also Equation 2.1. 6, 7, 9, 30, 39 spectral response function Describes relative sensor (channel) sensitivity to different parts of the spectrum. 9, 10, 15, 37, 39
58
Glossary
Sun-synchronous The plane of a sun-synchronous orbit is constant relative to the Sun. See also subsection 2.2.4. 12, 13, 15, 57 window region The window region refers to terrestrial radiation emitted at wavelengths of 8 μm to 12 μm. In this region, no radiation is significantly absorbed by gases and radiation is emitted to space under clear-sky conditions. 8, 24
Acronyms
AMSU Advanced Microwave Sounding Unit. 3, 4, 10, 11, 16, 17, 19, 21, 42, 43, 45, 55 ANN Artificial Neural Network. 3, 38, 42 AR4 4th Assessment Report. 2 ARTS Atmospheric Radiative Transfer Simulator. iii, 3, 4, 10, 29, 31, 33, 37, 39, 40, 44, 55 AVHRR Advanced Very-High Resolution Radiometer. 9, 10, 14, 15, 19, 44–46, 55 CALIPSO Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation. 18 CPR Cloud Profiling Radar. 3, 18, 21, 42, 45, 55 CTH Cloud Top Height. 27, 55 CTP Cloud Top Pressure. 27, 56 CTT Cloud Top Temperature. 27, 56 DDA Discrete Dipole Approximation. 35 DMSP Defense Meteorological Satellite Programme. 15, 16, 45 DOIT Discrete Ordinate ITerative. 36, 37, 40 ECMWF European Centre for Medium-range Weather Forecasting. 38, 59 ERA ECMWF Re-Analysis. 38 ESMR Electrically Scanning Microwave Radiometer. 15 FDTD Finite Difference Time Domain. 35 FRAC Full Resolution Area Coverage. 15 GAC Global Area Coverage. 15 GCM general circulation model. 38 HIRS High resolution Infrared Radiation Sounder. 4, 10, 11, 14, 19, 21, 39, 42, 44, 45, 56 59
60
Acronyms
HITRAN HIgh resolution TRANsmission. 33, 56 IPCC Intergovernmental Panel on Climate Change. 2 IR Infra-Red. 7 IWC Ice Water Content. 26, 56 IWP Ice Water Path. 2, 3, 26, 27, 38, 42, 45, 56 IWSSM International Workshop on Space-based Snowfall Measurement. 18, 19 LTAN Local Time Ascending Node. 13, 18, 43, 57 MC Monte Carlo. 36, 37, 40, 44 MHS Microwave Humidity Sounder. 3, 4, 16, 19, 21, 41–43, 45, 57 MSPPS Microwave Surface and Precipitation Products System. 42, 45 MSU Microwave Sounding Unit. 15 NESDIS National Environment Satellite, Data and Information Service. 42, 45 NOAA National Oceanic and Atmospheric Administration. 3, 4, 10, 14–16, 18, 41–43, 45 PWV Precipitable Water Vapour. 17 SEVIRI Spinning Enhanced Visible Infra-Red Imager. 9, 46 SNO simultaneous nadir overpass. 4, 21, 43, 45, 57 SRF sensor response function. 9, 10 SSM/I Special Sensor Microwave/Imager. 15 SSM/T Special Sensor Microwave/Temperature. 15, 16 TIROS Television InfraRed Operational Sounder. 5, 6, 14, 15 TOA Top Of Atmosphere. 6, 7 TRMM Tropical Rainfall Measuring Mission. 17 UTH Upper Tropospheric Humidity. 4, 20 VHRR Very High Resolution Radiometer. 14
Paper I Collocating satellite-based radar and radiometer measurements — methodology and usage examples
Authors: G. Holl, S. A. Buehler, B. Rydberg, and C. Jiménez
Bibliography: G. Holl, S. A. Buehler, B. Rydberg, and C. Jiménez. Collocating satellitebased radar and radiometer measurements – methodology and usage examples. Atmos. Meas. Tech., 3:693–708, 2010. doi: 10.5194/amt-3-693-2010
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63 Atmos. Meas. Tech., 3, 693–708, 2010 www.atmos-meas-tech.net/3/693/2010/ doi:10.5194/amt-3-693-2010 © Author(s) 2010. CC Attribution 3.0 License.
Atmospheric Measurement Techniques
Collocating satellite-based radar and radiometer measurements – methodology and usage examples G. Holl1 , S. A. Buehler1 , B. Rydberg2 , and C. Jim´enez3 1 Department
of Space Science, Lule˚a University of Technology, Kiruna, Sweden of Radio and Space Science, Chalmers University of Technology, G¨oteborg, Sweden 3 Laboratoire d’Etude du Rayonnement et de la Mati` ere en Astrophysique, Centre National de la Recherche Scientifique, Observatoire de Paris, Paris, France 2 Department
Received: 29 January 2010 – Published in Atmos. Meas. Tech. Discuss.: 26 February 2010 Revised: 20 May 2010 – Accepted: 1 June 2010 – Published: 21 June 2010 Abstract. Collocations between two satellite sensors are occasions where both sensors observe the same place at roughly the same time. We study collocations between the Microwave Humidity Sounder (MHS) on-board NOAA-18 and the Cloud Profiling Radar (CPR) on-board CloudSat. First, a simple method is presented to obtain those collocations and this method is compared with a more complicated approach found in literature. We present the statistical properties of the collocations, with particular attention to the effects of the differences in footprint size. For 2007, we find approximately two and a half million MHS measurements with CPR pixels close to their centrepoints. Most of those collocations contain at least ten CloudSat pixels and image relatively homogeneous scenes. In the second part, we present three possible applications for the collocations. Firstly, we use the collocations to validate an operational Ice Water Path (IWP) product from MHS measurements, produced by the National Environment Satellite, Data and Information System (NESDIS) in the Microwave Surface and Precipitation Products System (MSPPS). IWP values from the CloudSat CPR are found to be significantly larger than those from the MSPPS. Secondly, we compare the relation between IWP and MHS channel 5 (190.311 GHz) brightness temperature for two datasets: the collocated dataset, and an artificial dataset. We find a larger variability in the collocated dataset. Finally, we use the collocations to train an Artificial Neural Network and describe how we can use it to develop a new MHS-based IWP product. We also study the effect of adding measurements from the High Resolution Infrared Radiation Sounder (HIRS), channels 8 (11.11 μm) and 11 (8.33 μm). This shows a small improvement in the retrieval quality. The collocations described in the article are available for public use. Correspondence to: G. Holl (
[email protected])
1
Introduction
Atmospheric remote sensing from satellites is a major source of data for the atmospheric sciences and for operational weather forecasting (Kidd et al., 2009). Measurements from Earth observation satellites have a global or near-global coverage. However, the accuracy of products derived from such measurements is often poor (Wielicki et al., 1995; Wu et al., 2009). A combination of observations from different instruments enables applications that are impossible with singleinstrument measurements. One way to combine measurements is through collocations. A collocation is an event where different (satellite) sensors observe the same location at roughly the same time. The collocations considered here are mainly between active measurements from the Cloud Profiling Radar on-board CloudSat, and passive measurements from microwave and infrared sensors on-board National Oceanic and Atmospheric Administration (NOAA)18. One product obtained by remote sensing measurements is the Ice Water Path (IWP), the vertically integrated Ice Water Content (IWC) or the column mass density of ice in the atmosphere. Ice clouds are important for the climate, because they absorb and scatter thermal radiation and reflect solar radiation, and thus influence the radiation budget of the Earth (Stephens, 2005). As shown by John and Soden (2006), different General Circulation Models (GCMs) disagree by an order of magnitude about the climatology of IWP. Also IWP values from remote sensing measurements differ considerably (Wu et al., 2009). Therefore, it is important to improve the quality of ice cloud retrievals. A good understanding of the cloud signal in microwave radiometer measurements is an important step in the development of retrieval algorithms for possible future missions, such as the Cloud Ice Water Submillimetre Imaging Radiometer (CIWSIR), proposed by Buehler et al. (2007).
Published by Copernicus Publications on behalf of the European Geosciences Union.
64 694 Collocations between sensors on the same platform are commonly used (for example, see Frey et al., 1996; Bennartz, 2000). The idea to collocate data from different satellite platforms is not new either. Wielicki and Parker (1992) compare the cloud cover obtained with sensors of different spatial resolution. The A-Train constellation was motivated by the advantages of using a combination of measurements (Stephens et al., 2002). Already before CloudSats launch, Miller et al. (2000) described how to use active sensor data as a priori information for passive sensor retrievals, anticipating “a considerable overlap of CloudSat with the Earth Observing System (EOS) PM and Geostationary Operational Environmental (GOES) satellites”. Several recent studies use the new possibilities from the A-Train (for example, Holz et al., 2008; Kahn et al., 2008). However, not much work has been published on actual collocation methods. The first publication on the subject appears to be a technical note written in Japanese (Aoki, 1980). Judging from the abstract, Aoki (1980) describes how to match AVHRR and HIRS/2 if the instruments are on the same satellite. Other conference papers on the subject are Nagle (1998) and Sun et al. (2006). The first peerreviewed publication on the subject appears to be Nagle and Holz (2009), discussed in more detail in Sect. 3.1.1. No literature exists that focusses on collocations between an active instrument such as the Cloud Profiling Radar (CPR) on-board CloudSat and passive, operational instruments on Polar Orbiting Environmental Satellites (POES) such as the MHS on the NOAA-18. However, such collocations have relevant applications. Although a satellite like CloudSat has high quality products, the coverage is small compared to operational satellites, and it will have a limited lifetime. If we can use collocations between CloudSat CPR and NOAA-18 MHS to improve the operational microwave IWP retrieval, the advantages will last much beyond the lifetime of the ATrain satellites and have a much higher spatial coverage. Even passive microwave data from before CloudSat could be reprocessed with an improved algorithm. Whereas Miller et al. (2000) describe a retrieval that requires collocated data for each individual retrieval, we show that collocations can be used to develop new retrievals, that can then be used for non-collocated passive radiometer measurements. The main purpose here is to study collocations between CloudSat CPR and NOAA-18 MHS. Collocations with MHS and AMSU-B on other POES were also located, but due to the large distances between the satellites, few useful collocations were found. Hence, the study focuses on NOAA18 MHS. The collocation procedure is described in Sect. 3. The secondary purpose of the study is to look at possible uses of the collocations. Three applications are described in Sect. 4. Firstly, the NOAA National Environmental Satellite, Data and Information Service (NESDIS) Microwave Surface and Precipitation Products System (MSPPS) IWP product is compared with the IWP product from the CPR on-board CloudSat (Sect. 4.1). Simulated radiances from generated clouds are used to study the relation between brightness temAtmos. Meas. Tech., 3, 693–708, 2010
G. Holl et al.: Collocations – methodology and usage perature and IWP, and compare this with the statistics of the collocated dataset (Sect. 4.2). Finally, in Sect. 4.3, we use microwave radiances, with and without infrared measurements, to train an Artificial Neural Network with the CloudSat IWP as a target. Such a network can then be used to develop a new IWP product from microwave (and IR) measurements. Such applications were not found in peer-reviewed literature.
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The Cloud Profiling Radar (CPR) is a radar instrument on-board the sun-synchronous CloudSat satellite (Stephens et al., 2002), launched 28 April 2006. It has an operating frequency of 94 GHz and measures profiles of backscattering ratio at a 0.16◦ off-nadir angle. CloudSat generates a profile every 1.1 km along-track. A profile footprint is 1.3 km across-track and 1.7 km along-track. A profile is taken every 0.16 s. CloudSat is part of the A-Train constellation. It has an inclination of 98.26◦ and a Local Time Ascending Node (LTAN) varying between 13:30 and 13:45 local solar time. We use the ROIWP (Radar-Only Ice Water Path) field from the 2B-CWC-RO (level 2b, Cloud Water Content, Radar Only) product, version 008. Austin et al. (2009) describe the algorithm to calculate IWC from radar reflectivity profiles. They report an upper limit of the uncertainty of 40%. However, throughout this article, we assume CloudSat CPR to represent the truth since it is supposed to provide the most accurate measurements of IWP. The data originate from the CloudSat Data Processing Center. All measurements are geolocated and time-associated. The Advanced Microwave Sounding Unit-B (AMSU-B) and its successor the Microwave Humidity Sounder (MHS) are microwave radiometers (Saunders et al., 1995; Kleespies and Watts, 2007). MHS channels 3–5 correspond to AMSUB channels 18–20. We use the MHS channel numbers. Channel 3 has a centre frequency of 183.31±1.00 GHz with a bandwidth of 500 MHz, channel 4 has a centre frequency of 183.31±3.00 GHz with a bandwidth of 1000 MHz, and channel 5 has a centre frequency of 183.31±7.00 GHz (AMSUB) or 190.31 GHz (MHS) with a bandwidth of 2000 MHz (AMSU-B) or 2200 MHz (MHS). We use channels 3–5 because of the prominent water vapour spectral line at 183.31 GHz. In this article, we neglect the differences between AMSU-B and MHS. Although they are not the same, the standard deviation of the difference is much larger than the mean difference, so that a simple correction is not possible (Kleespies and Watts, 2007). Because of its proximity to CloudSat, we focus on NOAA-18 and MHS for the collocations. However, we have also looked for collocations with MetOp-A (a satellite operated by the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT)), NOAA-15, NOAA-16 and NOAA-17, so with a total of five satellites. The MHS field of view is www.atmos-meas-tech.net/3/693/2010/
65 G. Holl et al.: Collocations – methodology and usage around 1.1◦ , and the footprint size at nadir is around 15 km in diameter. It scans across-track in angles from −49.44◦ to 49.44◦ with 90 measurements per scan line. A scan takes 8/3 s. MHS is currently present on NOAA-18, NOAA-19 and MetOp-A, whereas AMSU-B is present on NOAA-15 through NOAA-17. All those satellites are sun-synchronous satellites. NOAA-18 has an inclination of 98.74◦ and a LTAN of 13:391 . This is close to CloudSat, which leads to a large number of collocations, as described later in the article. MHS measures the antenna temperature, which can be calibrated to obtain a brightness temperature in units of Kelvin. We use the ATOVS and AVHRR Pre-processing Package (AAPP) software package to apply this calibration, described by Labrot et al. (2006) (ATOVS stands for Advanced TIROS Operational Vertical Sounder, where TIROS stands for Television InfraRed Observation Satellite). We obtain the radiances from the NOAA CLASS archive. All those satellites also carry the infrared radiometer High Resolution Infrared Radiation Sounder (HIRS), either HIRS/3 or HIRS/4. HIRS measures in 20 channels, one visible and nineteen infrared. We use channels 8 (λ = 11.1 μm, a window channel) and 11 (λ = 7.33 μm, a humidity channel) because ice clouds are clearly visible at those wavelengths. HIRS/3 is present on NOAA-15 through NOAA-17 and HIRS/4 is present on NOAA-18, NOAA-19 and MetOpA. HIRS scans the atmosphere in 56 angles between −49.5◦ and 49.5◦ . Those measurements are not on the same grid as the MHS measurements (see Fig. 1). A HIRS scan takes 6.4 s. 3
Finding collocations
The footprint size of the considered sensors is in the order of kilometres, whereas the measurement duration is in the order of milliseconds. The spatial extent of a measurement is of the same order as the physical extent of a cloud or larger (kilometers), but the time order of a measurement (fraction of a second) is much smaller than a typical cloud lifetime (minutes to hours) (Rogers and Yau, 1979). Thus, to have a meaningful collocation, the footprints need to have a physical overlap. However, the time between the measurements can be much larger than the duration of a measurement. Hence, a collocation occurs when the sensors observe exactly the same place at approximately the same time. As shown in Fig. 1, an MHS footprint is an order of magnitude larger than a CPR footprint and HIRS measurements are not on the same grid as MHS measurements. We create two collocated datasets. In the first dataset, there is an entry for each CloudSat measurement collocating with an MHS measurement, so that there can be many collocations for the same MHS pixel. In the second dataset, each collocation has a unique MHS measurement and CPR pixels are 1 As of 5 February 2009 00:00:00 from the Polar Orbiting Environmental Satellites (POES) Spacecraft Status website.
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averaged. For each MHS measurement, we note the number of CPR pixels inside the MHS pixel, the average CPR IWP value, the standard deviation of the CPR IWP and the fraction of cloudy CPR pixels. For the averaging, we consider the CPR pixels as point measurements and the MHS pixels as circular measurements with a radius of 7.5 km and a constant sensor spatial response function inside this area. In reality, the sensor spatial response function of MHS is better approximated by a Gaussian shape. Although this might reduce the representativeness, this effect is small compared to other error sources. The total area covered by the CPR pixels is still much smaller than the MHS footprint area. This leads to a sampling error, as discussed in Sect. 3.3 below. Both datasets are available for public use. 3.1
Collocation finding procedure
The collocation finding procedure consists of four steps. The steps are described in detail in the following text. 1. Orbits (granules) with time overlap are selected. 2. Orbit sections are selected according to a rough temporal criterion. 3. Measurements possibly fulfilling the spatial criterion are selected. Atmos. Meas. Tech., 3, 693–708, 2010
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4. The temporal criterion is applied to the selected measurements.
1. The distance in km between successive points of the ground track is computed for both ground tracks, considering only the segments screened according to the temporal criterion discussed above. The maximum speed of the ground tracks is assumed to be the maximum distance. Atmos. Meas. Tech., 3, 693–708, 2010
distance (km)
The measurement data as obtained from the data providers is stored as one file for each orbit. Those files, known as granules, contain geolocated, time-referenced measurements. The geolocation refers to the actual measurement; the position of the satellite is not available and not required for the procedure (in contrast to Nagle and Holz (2009) discussed further down). The filenames contain information about the starting and ending time of the data contained by the granule. For each CPR granule, we locate all NOAA and MetOp granules that have a time overlap with the CPR granule. Those are two granules for each POES for each CPR granule, or a total of ten files for each CPR granule to search for collocations (MetOp-A and NOAA-15 through NOAA-18). We read the CPR file along with each of the associated POES files. The start and end times of the files are different. The segment with time overlap is selected, plus the segment where the time difference is less than the maximum time interval for a collocation to be considered. For example, if the CPR granule covers 10:00–11:30 UT, and a POES granule covers 11:00–12:30 UT, and our maximum time difference is 15 min, we consider the data in the interval 10:45–11:45, or more precisely 10:45–11:30 in the CPR granule and 11:00– 11:45 in the POES granule. As defined above, a collocation has a spatial and a temporal criterion. We use a two-step approach: first we look for any collocations that might meet the spatial criterion, and then whether those also meet the time criterion. Starting from the orbit data screened according to the first temporal criterion as explained above, we find the measurements that meet the spatial criterion. In the first step, we do not consider the true pixel size or the sensor spatial response function of either sensor. Instead, we treat the measurements as points and define a maximum distance to select the measurement pair for further consideration. The sensor spatial response function and the effective field of view can be used later to select a subset of those collocations or a weighting of them to consider the MHS spatial response function. We consider the ground track of each scan angle of the MHS (track A) and compare it to the single scan in the CPR (track B), but the following procedure works as well if both instruments are scanning. If two ground tracks are plotted, a human observer can see immediately whether there is any spatial overlap or not. Computers can not, so the following algorithm is used to identify points where the spatial overlap condition is met.
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Fig. 2. Illustration of collocation principle. For this example, we consider the CloudSat granule starting 6 January 2007 at 01:10 UTC and the MHS granule starting at the same date at 00:26 UTC. The figure shows the distance from pixel number 11166 from the CloudSat granule to all MHS pixels at a viewing angle of −0.56◦ . The crosses show twenty equally spaced samples and the thick line shows the super-interval to be searched for collocations. Refer to the text for further explanation.
2. Start with n = 1. 3. Find close points to An in B. Here, An is the n-th measurement in track A. Figure 2 shows the distance from a CloudSat CPR pixel to all pixels in a MHS track for a fixed viewing angle. If any collocations exist, they will be close to the global minimum. Find points meeting the distance criterion by the following method. (a) Choose N equidistant points (henceforth samples) from B as shown in Fig. 2. Combined with the first and the last point of the track, the samples define the edges for N + 1 intervals. All intervals contain the same number of points, with the exception of the last interval, that may contain less points than the others. (b) Find which sample is closest to An . Call this sample Bm . (c) Consider Bm+1 ,Bm+2 ,···,Bm+r where Bm+r is the first sample that does not meet the spatial condition or the last measurement point of the granule. Consider Bm−1 ,Bm−2 ,···,Bm−l where Bm−l is the first sample that does not meet the spatial condition or the first point of the granule. If N is large enough, all points that meet the spatial criterion are contained by the super-interval (Bm−l ,Bm+r ), because the minimum of the distance from An to B will be contained by it (if N is too small, this interval www.atmos-meas-tech.net/3/693/2010/
67 G. Holl et al.: Collocations – methodology and usage may contain only a local minimum). An example of such a super-interval is shown by the thick line in Fig. 2. Consider this super-interval. (d) Calculate the distance between An and every point in the super-interval. (e) Note all points for which the spatial condition is met. If there are no such points, remember the distance of the closest point. As shown in Fig. 2, N = 20 is already sufficiently large to guarantee that any points in B meeting the spatial criterion are contained in the super-interval. However, with N = 20 the number of points in the super-interval for which the distance to An will be calculated is still quite large. A larger N means the super-interval will be smaller, but the number of samples for which the distance will be calculated will be larger. The choice of N is thus an optimisation problem to reduce the number of distance calculations. We have chosen N = 200. 4. If there were any points for with the spatial condition was met, increase n by 1 and start again from 3. 5. If there were no points for which the spatial condition was met, calculate the least number of points remaining before it could be met: increase n by smallest distance − spatial condition max speed and start again from 3. For example, if the shortest distance is 120 km, the spatial condition distance 20 km, and the max speed 10 km/point, n will be increased by 120−20 = 10. 10 This works, because if the minimum distance from An to B is 120 km and the distance between An and An+10 is 100 km, the maximum distance between An+10 and B cannot be less than 20 km. The procedure described above is not the fastest possible (for example, point (d) could be optimised further) but with this algorithm, the bulk of the time running the code searching for collocations was spent on downloading files from a local server and decompressing them. From all points obtained with the procedure described above, those for which the time difference is less than 15 min are selected. Even though many of those CPR measurements are outside the MHS pixel, all are stored in the collocated dataset, because the MHS pixel size is a function of the scan angle, and some applications may allow for the CPR pixel to be (just) outside the MHS measurement. Also, it is cheap to select a subset of collocations, but to find pixels slightly further away than the initial criterion, the algorithm would need to be rerun.
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697 For each collocation and for each sensor (CPR, MHS, HIRS and AMSU-A), we store the location (lat/lon), the measurement time, the time of the first measurement in the file (to help finding the file containing the measurement) and the location of the point inside the datafile (row/column). We also store the distance of each centerpoint to the CPR centerpoint, and the time difference (MHS time minus CPR time). With this information, one can find exactly which of the CPR pixels fall inside the MHS pixels, possibly considering the sensor spatial response function. For the second dataset, we collect the CPR pixels in an MHS pixel and calculate the number of CPR measurements, the average, the standard deviation and the coefficient of variation (standard deviation divided by mean) of the IWP product. Here, we choose a circular MHS pixel area with a radius of 7.5 km, so we are certain that the CPR pixels are contained by the MHS pixel independently of the scan angle. We also note the cloud fraction, defined as the number of CPR pixels with at least 1 g m−2 of ice divided by the total number of CPR pixels inside the MHS measurement. 3.1.1
Comparison with Nagle and Holz (2009)
The method described above is quite different from the method described by Nagle and Holz (2009), henceforth referred to as “NH”. NH divide the two instruments to be collocated into a master and a slave, where the small slave observations are projected on the large master footprint. They find the location of the satellites as a function of time (forward navigation) and “estimate the time at which a slave satellite passes abeam of a master FOV on the surface” (inverse navigation). They then calculate simultaneous nadir observations (SNO), when two satellites pass over any point on the ground within a certain time window. For this calculation, NH use an orbital prediction model. They search the scan lines around the SNO for overlap with the master FOV. NH assign weights to each of the slave observations based on the sensor spatial response function of the master. NH claim that their method works for any combination of satellite, aircraft and ground observations. However, a scanning instrument might very well collocate with a ground observation without any SNO if the measurement is strongly off-nadir. For (near)-parallel orbits, this can be the case between different satellites as well. In fact, at one point NH “presuppose that the two orbital planes are not nearly coincident”. NH use the satellite position to calculate the projected sensor spatial response function on the Earth surface. We use an expression from Bennartz (2000) to calculate the size of the pixel, and we do not presently consider the sensor spatial response function.
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NH was designed to be computationally efficient and may very well be faster than our method. However, our method is conceptually simpler than NH. Our method does not require any forward or inverse navigation. It finds collocations regardless of the presence of simultanuous nadir observations. For some applications, only simultanuous nadir observations are of interest; in this case, NH and our method should give the same result. The processing of slightly more than two years of data from CloudSat and five AMSU/MHS sensors with our methods took around two weeks of computer time on a powerful workstation (Intel Xeon Dual Quadcore 3.20 GHz, 16 Gigabyte Random Access Memory (RAM)). Most of this time was due to transferring files over the network and decompressing them. We did not carry out a comparison of speed and results using a common set of source data.
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We have located collocations for the period between 15 June 2006 13:12 and 4 October 2008 10:34. For the year 2007, we have found 124 822 977 collocations between the NOAA-18 MHS and the CloudSat CPR, where the maximum distance between MHS and CPR centre points did not exceed 15 km and the time difference between MHS and CPR measurements was limited to 15 min. With a maximum distance of 7.5 km and counting the MHS pixels, the number of collocations reduces to 2 669 135. If only tropical nadir points are selected (within 30 degrees of the equator, within 1 degree of nadir), around 1% or 26 410 MHS pixels remain. Figure 3 shows the latitudes at which collocations occur between the CloudSat CPR and the MHS/AMSU-B on different satellites. It shows that only the NOAA-18 MHS has collocations with the CPR globally. This is due to the fact that the LTAN of the NOAA-18 (13:39) is always similar to the CloudSat LTAN (13:30–13:45). NOAA-18 is near the ATrain constellation and thus near CloudSat, because CloudSat is part of the A-Train. All other POES considered in this study have collocations with CloudSat CPR only near the poles. Figure 4 shows at which angles and latitudes the collocations occur. At the equator, no nadir collocations with a time difference of less than one minute occur. Rather, the viewing angle is sligthly off-nadir. If two satellites pass through the same place in space2 with one minute in between, the Earth rotates so their subsatellite points are roughly 1 m/24 h·40 075 km≈27.8 km apart. For a NOAA18 altitude of 850 km, the viewing angle then needs to be tan−1 (27.8/850) = 1.9◦ . In reality, the satellites do not pass through the exact same point, and the viewing angles for collocations within one minute are slightly larger. The CloudSat has a slightly lower inclination than NOAA-18, so for a 2 The same place in space in an Earth-centered inertial reference system.
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Fig. 3. A histogram of the number of collocations between the CloudSat CPR and the AMSU-B or MHS sensors on various satellites in January 2007. The maximum distance for a collocation is 15 km; the maximum time between the collocated measurements is 15 min (900 s). The number of collocations refers to the number of CPR pixels collocating with an AMSU-B or MHS pixel.
collocation to occur, NOAA-18 has to look to the left when it reaches its northernmost point and to the right when it reaches its southernmost point. CloudSat and NOAA-18 are in some sort of “orbital resonance”, as shown in Fig. 5, showing the collocations in January 2007. Figure 5 shows a time series of the number of collocations per hour, where the upper left is 1 January, 00:00–00:59 and the lower right is 31 January, 23:00–23:59 (inclusive). The figure shows a collocation pattern with a 56-h period: 16 h with collocations, 40 h without. 3.3
Sampling effects
As shown in Fig. 1, an MHS footprint is an order of magnitude larger than a CPR footprint. The smallest MHS pixel is the nadir-viewing pixel, which has a diameter of 16 km. The CPR pixel can be approximated by an ellipse of 1.3 by 1.7 km2 . It covers at most 0.65% of the area an MHS pixel: π 1.3 1.7 ACPR = 2 2 2 = 0.0065 = 0.65% AMHS π 16 2 Many CPR measurements fit in one MHS measurement. Since the CPR is not a scanning instrument, CPR pixels never fill an MHS pixel completely. In the best case, a nadir MHS pixel contains around 15 CPR pixels (or only 13 when we limit the collocations to CPR pixels within 7.5 km of the MHS centrepoint). The total area is less than 15 · 0.65% = 9.75% because of the overlap between subsequent CPR pixels. Usually, the CloudSat ground track does www.atmos-meas-tech.net/3/693/2010/
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not pass through the centre of the MHS pixel, and the situation is worse. Hence, sampling effects need to be taken into consideration. A collocation is considered representative, or good, if the CPR IWP statistics for the area covered by CPR are the same as the statistics of a hypothetical CPR IWP covering the full MHS pixel. CPR pixels inside the MHS pixel have the same statistics as they would if they would fill the entire MHS pixel. Whether the collocation is representative cannot be known exactly, because high-resolution information on the part of the MHS pixel not covered by CPR pixels is not available in this approach. However, we can look at some indicators to make an educated guess as to how well the CPR pixels represent the MHS pixel. Figure 6 shows three graphs that give some insight in the sampling error. The MHS pixel is assumed to be circular with a radius of 7.5 km. In Fig. 6a we can see that most collocations contain a relatively large number of CPR pixels, but many do not. When the number of CPR pixels inside the collocation is small, the CPR pixels are close to the MHS footprint edge and poorly represent the MHS pixel. The highest number of CPR pixels inside a MHS pixel occurs when the CPR groundtrack passes close to the centre of the MHS footprint. This is the optimal case. Figure 6b shows a histogram of the coefficient of variation of the CPR IWP product for the CPR pixels within 7.5 km of the MHS centrepoint. A small coefficient of variation corresponds to a homogeneous cloud. The more homogeneous the cloud, the more representative the CPR pixels are for the complete MHS footprint area. We use the coefficient of variation rather than the standard deviation because the standard www.atmos-meas-tech.net/3/693/2010/
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deviation is likely to be much larger for clouds with a high IWP than for clouds with a low IWP. Selecting collocations based on the standard deviation would throw away many of the measurements with high IWP. The coefficient of variation is largest when some CPR pixels measure a strong cloud and others do not measure any cloud at all. This indicates the presence of a strong, localised cloud, which significantly reduces our trust in the representativeness of the CPR pixels. In Fig. 6c, the distribution of CPR inside MHS is shown for three cases. The red dots show a case with an extremely high coefficient of variation (2.106; note in panel (b) that a coefficient of variation larger than 2 is so rare that it is not visible in the histogram). Since a thick cloud that is only 1 km in diameter is unlikely, this happens usually when the cloud is just on the edge of the MHS pixel. In either case, the CPR pixels do probably not share the same statistics as the MHS footprint and the collocation is not useful. The green dots show a case with a very low coefficient of variation (0.017; cases where all CPR pixels have the same nonzero measurement and the coefficient of variation is 0 occur as well, but the IWP value tends to be 1 g m−2 so it would not be visible in this graph). The portion of the cloud imaged by CPR has a roughly constant IWP of around 70 g m−2 . It is quite likely that the rest of the MHS pixel looks similar. The example in blue shows a collocation with a coefficient of variation of 0.354. When the criteria discussed above are applied, sampling effects are reduced and a large number of collocations remain.
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Fig. 6. Some collocation properties for 2007. (a) shows a histogram of the number of CPR pixels that fit inside a MHS pixel (circular with a 7.5 km radius). (b) shows a histogram for the coefficient of variation of all collocations that contain only cloudy pixels. (c) shows examples of how CPR IWP may be distributed inside a MHS pixel. See text for a discussion.
4
Applications
Collocations can be used in many different ways. This section presents some possible applications of collocations between CloudSat CPR and NOAA-18 MHS. Three examples are explored in the following subsections. This section is meant to show what can be done with such a collocated data set and does not provide a comprehensive study of the different applications. 4.1
Comparison with NESDIS IWP
Various algorithms exist to determine IWP from microwave radiometer measurements (Liu and Curry, 2000; Zhao and Weng, 2002; Weng et al., 2003). The National Environment Satellite, Data and Information Service (NESDIS) publishes an operational IWP product from MHS measurements in the Microwave Surface and Precipitation Products System (MSPPS). Zhao and Weng (2002) assume spherical ice particles and calculate the effective particle diameter from the ratio between the scattering at 89 GHz and 150 GHz. They assume a constant bulk volume density and calculate the IWP from this. They also discuss how errors propagate in the retrieval algorithm, but no discussion of systematic error and no validation for the NESDIS MSPPS IWP was found in this paper, nor elsewhere in the literature. Waliser et al. (2009) Atmos. Meas. Tech., 3, 693–708, 2010
find a dry bias in the NESDIS IWP product. They explain this from the Zhao and Weng (2002) screening criteria and the MHS insensitivity for ice particles smaller than 0.4 mm. CloudSat IWP has a systematic uncertainty of up to 40% (Austin et al., 2009). Judging from the available data, the detection limit for CloudSat IWP is 1 g m−2 . Figure 7 shows a comparison of the NESDIS MSPPS IWP with the CloudSat IWP. It shows that the NESDIS IWP is systematically smaller than the CPR IWP. For many nonzero CloudSat measurements, the NESDIS IWP is zero. This is because thin clouds are (almost) transparent for microwave radiation in the frequencies at which MHS operates (Greenwald and Christopher, 2002). For some NESDIS IWP measurements, the CloudSat IWP is zero. This happens due to the different footprint sizes. The MHS footprint is much larger than the CPR footprint. A cloud that does not cover a complete MHS pixel may be missed by the CPR (see Sect. 3.3). MSPPS IWP is systematically lower than CPR IWP by approximately 70–90%. Austin et al. (2009) estimate the CPR accuracy to 40%, based on a retrieval blind comparison study by Heymsfield et al. (2008), which was based on simulated radar observations for ice particle data from aircraft in-situ measurements. While the profiles considered in that study may not be representative for all atmospheric cases, we can www.atmos-meas-tech.net/3/693/2010/
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4.2
Comparison of BT-IWP relations
As a second application example, we investigate the relation between the MHS channel 5 brightness temperature and the associated Ice Water Path for two different datasets. The first dataset consists of the collocations, providing a mapping between brightness temperatures and independent IWP. The second dataset consists of a mapping generated from 30 000 synthetic atmospheres as described below. Note that this mapping predates the collocated measurements. Rydberg et al. (2009) use this method to derive IWC from the Sub-Millimetre Radiometer (SMR) on the Odin satellite. It can potentially be used to derive IWP from MHS. Atmospheric states, including clouds, are generated following the procedure described by Rydberg et al. (2009), and a brief overview is given here. Cloud states are generated in a series of steps, where two-dimensional (2-D) radar reflectivity fields from the Cloud Profiling Radar on-board CloudSat serve as the basis for obtaining realistic cloud structures. Orbit sections of CloudSat data (with a resolution of ∼ 250 m in vertical by 2 km along the scan line) are transformed to 3-D by inputting those into a stochastic iterative amplitude adjusted Fourier transform algorithm (Venema et al., 2006). This algorithm generates surrogate 3-D radar measurement fields with the same spatial resolution as the original fields. Cloud microphysical fields are generated in such a way that the surrogate 3-D radar reflectivity fields are conserved. This is done by assuming that spherical ice particles can be used to represent the single scattering properties of natural occuring ice particle populations. We lack information about the true shape of the ice particles, which is different for different cloud types, and the most generic assumption is to assume spheres. This is also the assumption made by Austin et al. (2009) for the CloudSat CPR IWP retrieval. The accuracy of this approximation is difficult to assess, because the true microphysical parameters are unknown. Furthermore, the cloud ice particle size distribution (PSD) parameterisation derived by McFarquhar and Heymsfield (1997) (hereafter MH97) is assumed to be the best representation of the tropical mean PSD. MH97 depends on temperature and ice water content (IWC), and is used to map radar reflectivity fields to IWC and PSD fields. However, it should be clear that local PSD may deviate significantly from MH97. For temperatures above 273 K, clouds are assumed to consist www.atmos-meas-tech.net/3/693/2010/
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still consider the CPR data to be considerably better validated than the MSPPS data. It is therefore likely that the difference reflects a real low bias in the MSPPS data. This is partly a fundamental problem, because of the transparency of thin clouds to radiation at MHS frequencies. However, MSPPS underestimates the IWP for thick clouds as well. A more accurate IWP product based on microwave measurements is probably possible. One way to obtain such a product is by using a neural network, described later in the article.
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Fig. 7. Two-dimensional histogram of CloudSat CPR Ice Water Path (averaged over an AMSU pixel) and NOAA NESDIS MSPPS IWP, for all collocations in the year 2007. The figure is similar to a scatter plot, but it shows the density of points rather than the actual points. Only measurements where either value is nonzero are shown. The black line shows the ideal case. The colour scale is logarithmic. See text for a discussion.
entirely of spherical water particles and the PSD of stratus cloud derived by Deirmendjian (1963) is used. Weather data (temperature, humidity, and pressure) and ozone information, originating from the European Centre for Medium-Range Weather Forecasts (ECMWF), are obtained from the CloudSat auxiliary data archive (ECMWF-AUX). ECMWF-AUX contains ECMWF state variable data interpolated to each CPR bin. These fields are handled as described by Rydberg et al. (2009) in order to have a realistic variability that accounts for variations on scales not resolved by ECMWF. Radiative transfer simulations of nadir viewing AMSU-B channel 20 (corresponding to MHS channel 5) are performed using version 1.1 of the Atmospheric Radiative Transfer Simulator (ARTS). This is a development of the first version, ARTS-1 (Buehler et al., 2005), where two scattering modules, a discrete ordinate iterative method (Emde et al., 2004) and a reverse Monte Carlo algorithm (Davis et al., 2005) have been implemented to solve the polarised radiative transfer equation. The Monte Carlo module is used and the 3-D variability of the atmosphere is fully considered in the radiance simulations. The lower and upper sidebands of AMSU-B channel 20 are represented by single frequencies of 176.01 and 189.91 GHz, respectively. For a diverse set of atmospheric profiles, the root mean square error between this approximation and a setup with a finer frequency grid is 0.020 K. The instrument antenna spatial response function is assumed to be a 2-D Gaussian with a full-width half-power beamwidth of 1◦ in both dimensions. Pencil beam simulations with a grid spacing matching the Atmos. Meas. Tech., 3, 693–708, 2010
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atmospheric states horizontal resolution are performed. After the antenna weighting the precision of the simulations is better than 0.5 K. The IWP is extracted along each pencil beam where radiative transfer simulations are performed. The atmospheric scenario has a higher spatial resolution than AMSU-B, so the simulated IWP are weighted according to the antenna pattern to obtain the AMSU-B IWP. Figure 8 shows a comparison between the two relations. We average the CPR IWP over the MHS pixel, and select a subset of collocations. For the collocations, only measurements that are within 20 degrees of the equator are used, in order to prevent a signal from the surface (Buehler and John, 2005). Only collocations where the MHS measurement is within 5 degrees of nadir are used, so that no significant limb effect occurs. Finally, collocations are selected where all CPR pixels are cloudy and the coefficient of variation is smaller than one, for reasons discussed in Sect. 3.3 above. The figure shows AMSU-B channel 20 or MHS channel 5 brightness temperature as a function of the IWP (logarithmic) for the two different datasets. In blue are the collocated measurements (MHS channel 5 and CPR IWP). The red boxes show simulated radiances for generated atmospheric states (AMSU-B channel 20 and generated IWP). The figure shows that both datasets have largely the same statistical features. For IWP up to around 100 g m−2 , the effect on the brightness temperature is minimal, because thin clouds are not resolved at MHS channels 3–5 frequencies (Greenwald and Christopher, 2002). For higher values of IWP, the brightness temperature decreases logarithmically as a function of IWP. For IWP >100 g m−2 , the simulated brightness temperatures are slightly higher than the observed ones. The microphysical assumptions for the generated atmospheric states are based on MH97, which differ from the assumptions in the CloudSat retrieval. This might contribute to the observed differences. Overall, the variability in the simulated brightness temperatures is smaller than the variability in the observed brightness temperatures. This effect is stronger for higher values of the IWP. Several factors may contribute to this discrepancy. The CPR pixels are much smaller than the MHS pixels, so the measured value is averaged over a smaller area. If a small, concentrated cloud exists inside a MHS pixel, the CPR might either see it, in which case it measures a higher IWP than the MHS, or it might miss it, so it measures a lower IWP. This adds to the variability. Additionally, the generated atmospheric states might not fully resolve the natural variabily of cloud microphysical parameters and of atmospheric temperature and humidity. 4.3
Developing a retrieval using neural nets
An artificial neural network (ANN) is an interconnected assembly of processing units called neurons (e.g. Jim´enez et al., 2003). Neural nets are widely used to statistically charAtmos. Meas. Tech., 3, 693–708, 2010
acterise the mapping between radiometric measurements and related geophysical variables (e.g. Krasnopolsky, 2007). We use an ANN to characterise the mapping between MHS radiances and the CPR IWP, and then use the trained ANN to retrieve IWP from the MHS measurements. We call this retrieval MHS-CPR IWP. MHS-CPR IWP has both advantages and disadvantages compared to other retrieval approaches. One can use a neural network with simulated rather than measured radiances, or one can use a more classical retrieval method. As we use the collocated measurements, an advantage is the relative simplicity; there is no need for a potentially complicated radiative transfer model with many possible sources of error. On the other hand, the collocations approach may introduce a number of errors, as discussed in Sect. 4.3.1. However, an MHS-CPR IWP can complement the other existing retrieval methods. The retrieval quality can never become as good as CloudSat, but the spatial and temporal coverage will be much larger. The neural network approach described below is in the exploration phase and will be developed further. We select a subset of collocations that provide a relatively homogeneous dataset. The subset is restricted to pixels over ocean within 20 degrees of the equator, because a warm (and humid) atmosphere prevents the MHS from getting a signal from the surface (Buehler and John, 2005). Due to these restrictions, the neural network is only applicable to the tropics. A strongly off-nadir measurement is colder due to the limb effect (Buehler et al., 2004). For the training, we restrict ourselves to measurements within 5 degrees of nadir. This avoids the need to compensate for this effect (described below). The neural network works for nadir measurements or measurements where the limb effect is compensated. As discussed in Sect. 3.3, the MHS measurement compromises a larger area than the CloudSat measurement, even when we average the CPR pixels inside an MHS pixel. If a small, strong event is present inside an MHS pixel, the CloudSat might miss it completely or measure exactly this event. In both cases, the observed MHS radiance is the same, but the CPR IWP can vary considerably. For that reason, we select only homogeneous measurements: the collocation shall contain at least ten CPR pixels, all measuring at least 1 g m−2 , and the standard deviation shall not exceed the mean value. The selection of only “cloudy pixels” for the training leads to a wet bias, because the neural network tends to the mean state if it has insufficient information from the input. We want to explore the effect of adding HIRS channels on the neural network retrieval. Hence, we choose collocations where at least five CPR pixels are within 10 km of the nearest HIRS pixel. Finally, only collocations where the time interval is at most ten minutes are selected. For the year 2007, we find 2627 collocations that meet the criteria described above. www.atmos-meas-tech.net/3/693/2010/
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703 In Fig. 9 we show an example of how a NN IWP product might look like. The data is for 1 January 2008. The left panels show the MHS brightness temperatures between 08:56 and 19:02 UTC, the right panel shows the IWP retrieved by the neural network.
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For the neural network calculations, we use the MATLAB Neural Network toolbox V6.0.1 (R2008b). The collocations are divided in 60% training, 15% testing and 25% validation. MHS channels 3, 4 and 5 are the inputs. As a target, we choose the log IWP which was found to work better than the ordinary IWP. The transformation is reversed after the application of the neural network. Throughout the process, CPR IWP is assumed to be the truth. The training is considered to be finished if the error with the testing data increases for fifteen consecutive iterations. After training, we store a neural network that we can then use for our retrieval. To compensate for the limb effect, we correct the brightness temperatures before we input them to the network. For each viewing angle and channel, the mean brightness temperature is calculated. We use only tropical measurements (within 30 degrees of the equator) to prevent an angledependent signal from Antarctica, which is mainly seen by one side of the scan. The limb effect is minimal for the two viewing angles closest to nadir. The average brightness temperature for those angles is the reference. The limb effect can be quantified by the difference between the reference brightness temperature and the mean brightness temperature for a certain viewing angle. We compensate for the limb effect by adding this difference to all measurements for this viewing angle.
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Error analysis
Four sources of error can be identified: (a) The CPR IWP uncertainty is up to 40% (Austin et al., 2009). This propagates directly into the MHS-CPR IWP. (b) Collocation mismatches add noise to the training data, as discussed in Sect. 3.3. This may or may not result in an error in the MHS-CPR IWP (noise in the input data need not change the best fit). (c) The inversion from MHS data inherently has a limited accuracy, leading to a significant uncertainty in the MHS-CPR IWP. (d) The MHS has a radiometric noise of up to 0.55 K and might suffer from calibration errors. Figure 10 shows a scatter plot between CPR IWP and collocated MHS-CPR IWP. Both axes are logarithmic. (a) and (d) do not contribute to the variability seen here. MHS-CPR IWP could still perfectly reproduce MHS-CPR IWP even considering the MHS radiometric noise, because this noise is part of the training data. If it would do so, CPR IWP might still be off by 40% compared with the true atmospheric IWP, but Fig. 10 would not show variability. The variability is consistent with simulations similar to the ones described in (Jim´enez et al., 2007). Since those simulations did not use collocations, the dominant source of the variability in Fig. 10 is likely to be the inversion error (c). For low IWP, the network exhibits a wet bias. Thin clouds are (almost) completely transparent at MHS frequencies (Buehler et al., 2007), so with only those measurements, there is no information for thin clouds. With no information, the neural network tends towards the mean state. Since only cloudy CPR pixels were used for the training, this explains the wet bias. Figure 11 shows the neural network sensitivity to MHS radiometric noise. A subset of tropical nadir measurements for 2007 are selected. For practical reasons, this subset consists of the MHS measurements for where collocations could be found; however, as the CloudSat values are not used for this figure, those measurements are effectively a sample of all MHS measurements for 2007. The figure shows the mean fractional IWP error as a function of IWP and input noise. For this figure, the neural network is applied twice. First, the unperturbed input data (MHS brightness temperatures for channels 3, 4 and 5) are fed into the ANN. This gives an unperturbed IWP for each measurement. Then, we add gaussian noise, starting with σ =0.1 K, to the input data, and feed this perturbed data to the ANN. This results in a perturbed For each collocation, the fractional IWP denoted by IWP. error is calculated as IWP IWP − 1. Those fractional errors are divided into bins according to the unperturbed IWP value. Atmos. Meas. Tech., 3, 693–708, 2010
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Fig. 9. The neural network (see text) can be used to retrieve IWP from radiances. The figure shows observations by NOAA-18 in the descending node on 1 January 2008 between 10:54 and 17:20 UTC (local time during the night). The left panels show the brightness temperatures as observed by the MHS channels 3–5. The right panel shows the IWP as generated with the neural network as described in the text. Cold areas in the left panel correspond to wet areas in the right panel.
For each bin, we calculate the mean fractional error. This process is repeated for higher values of σ , up to σ =2.0 K, taking steps of σ =0.1 K. Unsurprisingly, Fig. 11 shows that a higher input noise results in a higher error in the output. This effect is linear. The mean fractional error as function of IWP is less straightforward. The error is largest for IWP values of around 100 g m−2 and smaller for values that are either larger or smaller. This can be explained as follows. For small IWP, a small perturbation in the brightness temperatures has little influence on the IWP. The ANN does not interpret the brightness temperature noise as IWP. This is in line with the observation that thin clouds are transparent to the frequencies at which MHS operates (Greenwald and Christopher, 2002), and can also be seen in Fig. 8. For large IWP, MHS channels 3–5 will observe large depressions in brightness temperature, and a 2 K noise is much smaller than the signal, so its effect on the output is also small. However, for intermediate values of IWP, around 100 g m−2 , the noise is of a similar order of magnitude as the signal, and the ANN is Atmos. Meas. Tech., 3, 693–708, 2010
quite sensitive to input noise. The actual radiometric noise for MHS depends on the channel, but is always below 0.55 K (Kleespies and Watts, 2007). This means that radiometric noise is unlikely to be a dominant error source for this kind of IWP retrieval method. 4.3.2
Adding HIRS
Thin clouds are not visible by MHS channels 3–5 because the effect of ice clouds on microwave radiation at those frequencies is relatively small. In the infrared, the situation is different: even a small cloud has an observable effect, but an infrared sensor does not see the difference between a medium cloud and a thick cloud, because the sensor is saturated quickly (Jim´enez et al., 2007). Hence, we can expect the retrieval quality to improve if we combine infrared and microwave measurements. Figure 12 shows a scatter plot similar to Fig. 10, but with additional HIRS channels 8 and 11 (chosen for their clear cloud signal). The number of collocations used for the neural net remains the same, because we already preselected the www.atmos-meas-tech.net/3/693/2010/
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collocations so that at least five CPR pixels are less than 10 km from the nearest HIRS pixel centerpoint. By eye, it is hard to see whether there is any improvement gained by adding them. Figure 13 shows the fractional median error as a function of IWP for both cases. Here, the fractional median error is defined relative to CloudSat, so CloudSat is assumed to be true. The dashed line shows the error for the ANN where the input consists only of MHS channels, the dotted line shows the error for the ANN with an input consisting of MHS channels 3–5 and HIRS channels 8 and 11. For small values of IWP there is an improvement when adding the HIRS chanwww.atmos-meas-tech.net/3/693/2010/
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Fig. 13. Comparison of the median fractional error between independent and retrieved IWP, when only MHS channels are used or when both MHS and HIRS channels are used as input to the ANN. The median fractional error is defined as the median of all errors with a certain IWP, where the error is defined as IWP −IWP NN CPR . IWPCPR
nels. However, the error is still large, since a median relative error of 2 means that the retrieved IWP is on average a factor 2 off. For larger values of IWP, the errors are roughly the same, as expected. Why the retrieval does not strongly improve when adding HIRS is not yet fully understood. One factor may be the difference in footprint location for HIRS and MHS, even if only collocations with at least 5 CPR pixels in the HIRS pixel are considered. Additionally, HIRS might suffer from the Atmos. Meas. Tech., 3, 693–708, 2010
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beam-filling problem: the sensor may be saturated if only a part of the pixel is cloud-covered, and be unable to tell the difference between a partly cloudy and a fully cloudy pixel. A further investigation is necessary and will be carried out.
5
Conclusions
The collocation-finding method described in this work finds many collocations between the NOAA-18 MHS and the CloudSat CPR. Those collocations are frequent and globally distributed. Other POES collocations with CloudSat are limited to the polar areas. Sampling effects due to different footprint sizes need to be taken into consideration. There are numerous possible improvements to our procedure. The procedure to find the collocations can be refined by considering how the MHS footprint size depends on the scan angle. Even better, one can project the MHS sensor spatial response function onto the surface and calculate a weighted average of the collocated CPR pixels, similar to the procedure described by Nagle and Holz (2009). In comparison with Nagle and Holz (2009), our algorithm is relatively simple. For example, it does not need satellite position data. It finds collocations even in the absence of simultaneous nadir observations. Our method was designed for the case where one instrument is scanning and the other has a fixed viewing angle. It also works if both instruments are scanning, but in this case, it is slow and a different method is more suitable. If either satellite is geostationary or both instruments are on the same satellite, more optimised methods may be appropiate. The method does not depend on the nature of the sensor (active, passive) or the footprint size. The collocations have various applications. They can be used to compare different IWP products. As an example, we have compared the NOAA NESDIS MSPPS MHS IWP product against the CloudSat CPR IWP product. IWP values from the CloudSat CPR were found to be significantly larger than those from the MSPPS. This may be partly attributed because thin clouds are transparent to radiation at MHS frequencies, but since the MSPPS underestimates IWP even for high values, there should be room for improvement. As a second example, we have compared the IWP-BT relation for our collocations with the one for simulated radiances from synthetic atmospheric cases. The variability in the measured relation was found to be larger than the variability for the simulated relation. The validation for simulated radiances was performed statistically. A stronger validation would be to simulate the radiances for the exact cases where a collocation exists. As a final example, we have used the collocations to train an Artificial Neural Network to develop a new IWP product. We have shown that this method is promising. Finally, we have investigated the effect of adding HIRS channels 8 and Atmos. Meas. Tech., 3, 693–708, 2010
11 to such an ANN. Unexpectedly, this leads to only a small improvement in the retrieval quality. The IWP retrieval using an Artificial Neural Network looks promising, but requires additional work. We can improve the retrieval in various ways. One can make a stronger restriction for homogeneous scenes by looking at MODIS or AVHRR pixels inside the MHS, although this is limited as infrared measurements do not detect the vertical extent of the cloud. Another alternative is to combine MHS with other HIRS channels than those explored so far, or to directly input a combination of MHS and AVHRR for the training. On the other hand, the ANN might be extended to work for more measurements. By having more input parameters or multiple neural networks, the retrieval could work globally, One can extract additional information from other highresolution data, such as from the Moderate Resolution Imaging Spectroradiometer (MODIS; King and Greenstone, 1999) or the Advanced Very High-Resolution Radiometer (AVHRR; Cracknell, 1997). to better characterise the collocations. Those can be used to make a stronger estimate as to how homogeneous the scene observed by MHS is. All the applications can be expanded upon and many other applications can be developed. These and other issues will be adressed in further research. In particular, future work will focus on developing a global IWP product from passive microwave and infrared sensors available on operational polar orbiting satellites. The collocations are available for public use. Acknowledgements. The bulk of the work was carried out as part of the Master’s Thesis by first author Gerrit Holl. Thanks to the Spacemaster education programme for making this possible. We thank the people, organisations and institutes that have helped us to obtain the satellite data. Thanks to to Lisa Neclos for helping us with archived HIRS data, and to all involved with the NOAA CLASS archive for recent and current MHS, AMSU-B and HIRS measurements. Thanks to CloudSat for making available an accurate IWP product. We thank the UK MetOffice for providing the AAPP package and the ARTS radiative transfer community for its work on ARTS. We would also like to thank the National Graduate School in Space Technology at Lule˚a University of Technology. Thanks to the OpenStreetMap community for the freely useable map-data in Fig. 1. We would like to thank the AMT Editorial Board, associate editor Bernhard Mayer, and two anonymous reviewers, for their work in improving the article.
Edited by: B. Mayer
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78 708 Gaussian Bayesian retrieval of tropical upper tropospheric cloud ice and water vapour from Odin-SMR measurements, Atmos. Meas. Tech., 2, 621–637, 2009, http://www.atmos-meas-tech.net/2/621/2009/. Saunders, R. W., Hewison, T. J., Stringer, S. J., and Atkinson, N. C.: The Radiometric Characterization of AMSU-B, IEEE T. Microw. Theory, 43, 760–771, 1995. Stephens, G. L.: Cloud feedbacks in the climate system: A critical review, J. Climate, 18, 237–273, 2005. Stephens, G. L., Vane, D. G., Boain, R. J., Mace, G. G., Sassen, K., Wang, Z., Illingworth, A. J., OConnor, E. J., Rossow, W. B., Durden, S. L., Miller, S. D., Austin, R. T., Benedetti, A., Mitrescu, C., et al.: The Cloudsat Mission and the A-Train, Bull. Amer. Met. Soc., 83, 1771–1790, 2002. Sun, H., Wolf, W., King, T., Barnet, C., and Goldberg, M.: CoLocation Algorithms for Satellite Observations, in: 86th AMS Annual Meeting, this paper appears in the Proceedings of the 14th Conference on Satellite Meteorology and Oceanography, 2006. Venema, V., Ament, F., and Simmer, C.: A Stochastic Iterative Amplitude Adjusted Fourier Transform algorithm with improved accuracy, Nonlin. Processes. Geophys., 13, 321–328, 2006. Waliser, D. E., Li, J.-L. F., Woods, C. P., Austin, R. T., Bacmeister, J., Chern, J., Genio, A. D., Jiang, J. H., Kuang, Z., Meng, H., Minnis, P., Platnick, S., Rossow, W. B., Stephens, G. L., SunMack, S., Tao, W.-K., Tompkins, A. M., Vane, D. G., Walker, C., and Wu, D.: Cloud ice: A climate model challenge with signs and expectations of progress, J. Geophys. Res., 114, D00A21, doi:10.1029/2008JD010015, 2009.
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G. Holl et al.: Collocations – methodology and usage Weng, F., Zhao, L., Ferraro, R. R., Poe, G., Li, X., and Grody, N. C.: Advanced microwave sounding unit cloud and precipitation algorithms, Radio Sci., 38, 8068, doi:10.1029/2002RS002679, 2003. Wielicki, B. A. and Parker, L.: On the Determination of Cloud Cover From Satellite Sensors: The Effect of Sensor Spatial Resolution, J. Geophys. Res., 97, 12 799–12 823, 1992. Wielicki, B. A., Cess, R. D., King, M. D., Randall, D. A., and Harrison, E. F.: Mission to Planet Earth: Role of Clouds and Radiation in Climate, Bull. Amer. Met. Soc., 76, 2125–2153, 1995. Wu, D. L., Austin, R. T., Deng, M., Durden, S. L., Heymsfield, A. J., Jiang, J. H., Lambert, A., Li, J.-L., Livesey, N. J., McFarquhar, G. M., Pittman, J. V., Stephens, G. L., Tanelli, S., Vane, D. G., and Waliser, D. E.: Comparisons of global cloud ice from MLS, CloudSat, and correlative data sets, J. Geophys. Res., 114, D00A24, doi:10.1029/2008JD009946, 2009. Zhao, L. and Weng, F.: Retrieval of Ice Cloud Parameters Using the Advanced Microwave Sounding Unit, J. Appl. Meteorol., 41, 384–395, 2002.
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Paper II Understanding inter-satellite biases of microwave humidity sounders using global SNOs
Authors: V. O. John, G. Holl, S. A. Buehler, B. Candy, R. W. Saunders, and D. E. Parker
Accepted for publication in: Journal of Geophysical Research, 2011
© American Geophysical Union. Reproduced with permission.
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Understanding inter-satellite biases of microwave humidity sounders using global simultaneous nadir overpasses Viju O. John1, Gerrit Holl2, Stefan A. Buehler2, Brett Candy3, Roger W. Saunders3, David E. Parker1 Abstract. Simultaneous nadir overpasses (SNOs) of polar-orbiting satellites are most frequent in polar areas, but can occur at any latitude when the equatorial crossing times of the satellites become close owing to orbital drift. We use global SNOs of polar orbiting satellites to evaluate the inter-calibration of microwave humidity sounders from the more frequent high latitude SNOs. We have found based on sensitivity analyses that optimal distance and time thresholds for defining collocations are pixel centres less than 5 km apart and time differences less than 300 seconds. These stringent collocation criteria reduce the impact of highly variable surface or atmospheric conditions on the estimated biases. Uncertainties in the estimated biases are dominated by the combined radiometric noise of the instrument pair. The effects of frequency changes between different versions of the humidity sounders depend on the amount of water vapor in the atmosphere. There are significant scene-radiance and thus latitude dependencies in the estimated biases and this has to taken into account while inter-calibrating microwave humidity sounders. Therefore, the results obtained using polar SNOs will not be representative for moist regions, necessitating the use of global collocations for reliable inter-calibration. find simultaneous nadir overpasses (SNOs) of polar orbiting satellite pairs and use them for inter-calibration. There are regular near-polar SNOs and during an SNO, similar instruments on the different satellite platforms measure radiation emitted from the same area of Earth and/or its atmosphere at the same time. Therefore, any difference in the radiance measured by the satellites can be used to inter-calibrate the measurements. This is being developed in support of the Global Space-based Inter-Calibration System (GSICS) initiative to provide climate quality satellite datasets [Goldberg et al., 2011]. SNO data have been proven useful for inter-calibration of instruments such as HIRS and MSU/AMSU-A [e.g., Zou et al., 2006; Wang et al., 2007; Cao et al., 2005; Iacovazzi and Cao, 2007; Shi et al., 2008]. However, Iacovazzi and Cao [2008] showed that for those channels which are sensitive to the Earth’s surface, there are large uncertainities in the estimated inter-satellite bias due to surface inhomogeneity which arises mainly from variable surface emissivity of SNO scenes at sub-pixel scales. The concerns expressed by Iacovazzi and Cao [2008] can be put in the context of microwave humidity sounders as follows. The peak emission for a sounding channel occurs at an atmospheric level for which the optical depth, integrated from the top of the atmosphere, becomes approximately one [e.g., Petty, 2006]. Therefore, depending upon the amount of water vapor in the atmosphere, the peak emission levels of humidity sounding channels move up and down, in contrast to temperature sounding channels which use the absorption of well mixed gases such as oxygen or carbon dioxide. Thus the sounding height of a humidity channel is at its maximum in a wet tropical atmosphere and becomes lower as the satellite moves towards higher latitudes. Figure 1 shows how the total opacity, which is the vertically integrated absorption coefficient, varies as a function of the amount of water vapor in the atmosphere. For the dry atmospheres sampled by SNOs which normally occur between 70◦ and 80◦ latitudes [Cao et al., 2004], the opacity is of order one even for the channel closest to the 183.31 GHz water vapor line centre. Analysis of ERA-Interim [Dee et al., 2011] fourtimes daily precipitable water vapor data for 2010-01 and 2010-07 showed that more than 50 % of the values are below 3 mm at latitudes 70–80◦ except for the Arctic region in
1. Introduction Tropospheric humidity measurements from microwave humidity sounders such as Advanced Microwave Sounding Unit-B (AMSU-B; Saunders et al. [1995]) and Microwave Humidity Sounder (MHS; Bonsignori [2007]) have been proven to have significant impact on the skill of Numerical Weather Prediction [Andersson et al., 2007]. This is primarily due to their ability to measure humidity under all-sky conditions compared to clear-only sampling by infrared sounders [e.g., John et al., 2011]. Recently, some attempts have also been made to use microwave humidity sounding data for climate applications [e.g., Xavier et al., 2010; Eymard et al., 2010; Buehler et al., 2008]. However, although microwave temperature sounding data have been inter-calibrated and extensively used for climate studies [Thorne et al., 2010], this has not yet been done for the humidity sensors. The main reason for this is the short span of the data, primarily since late 1998; although Special Sensor Microwave Humidity Sounder (SSM/T-2) data began in 1994, these early measurements were not widely used except for research [e.g., Miao et al., 2001; Selbach et al., 2001; Sohn et al., 2003; Chung et al., 2011]. The error characteristics of SSM/T-2 radiances data are not fully understood, and careful validation is essential before they can be used to assess, in particular, long term trends in upper tropospheric water vapor which is an important climate variable, yet poorly simulated by current climate models [e.g., John and Soden, 2007]. Unfortunately, there is a lack of stable and reliable ground based or in situ reference measurements of atmospheric humidity to inter-calibrate satellite instruments [Seidel et al., 2009]. Cao et al. [2004, 2005] have developed a method to 1 Met
Office Hadley Centre, Exeter, UK of Technology, Kiruna, Sweden Met Office, Exeter, UK
2 Lule˚ a University 3 UK
Copyright 2011 by the American Geophysical Union. 0148-0227/11/$9.00
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Figure 1. Total opacities for 7 profiles with 0.2, 0.5, 1.0, 3.0, 10.0, 37.5, and 66.5 mm precipitable water vapor. These profiles are taken from the Chevallier et al. [2006] data set. The 37.5 mm corresponds to the median and 66.5 mm corresponds to the 95th percentile. Shaded regions represent the pass band positions of AMSU-B channels. The channel numbers are printed below the pass bands. Note that for MHS, Channel 2 is centred at 157 GHz (instead of at 150 GHz for AMSU-B) and Channel 5 has only one pass band at 190.31 GHz. Figure adapted from John and Buehler [2004].
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The Advanced Microwave Sounding Unit-B (AMSU-B) and the Microwave Humidity Sounder (MHS) are 5 channel microwave radiometers. They are designed to measure the radiation emitted from the Earth’s surface and atmosphere in order to estimate global fields of tropospheric humidity. The microwave absorption characteristics of the atmosphere are shown in Figure 1 and the instrument specifications are given in Table 1. AMSU-B is onboard NOAA-15 (N15), N16, and N17 and MHS is onboard N18, N19 and MetOpA (MA). Channels 1 and 2 at 89 GHz and 150 GHz (at 157 GHz for MHS), enable deeper penetration through the atmosphere to the Earth’s surface. Channels 3–5 are located in the strongly opaque water vapor absorption line at 183.31 GHz and provide information on the atmospheric humidity at different levels. The passbands of Channels 3, 4, and 5 are at 183.31±1.00 GHz, 183.31±3.00 GHz, and 183.31±7.00 GHz (only at 183.31+7.00 GHz for MHS), respectively. The passbands of the channels are also shown in Figure 1. Note that the 5 channels on AMSU-B are formally numbered as Channels 16–20 (Channels 1–15 belong to AMSU-A which is a temperature sounding instrument), but in this article we call them Channel 1–5 to be consistent with MHS channel numbers. At each channel frequency, the antenna beamwidth is a constant 1.1 degrees (full width at half maximum). Ninety contiguous cells are sampled on the Earth’s surface, with each scan covering ±49.5 degrees on each side of the subsatellite point. These scan patterns and geometric resolution translate to a 16.3 km diameter cell at nadir at a nominal altitude of ∼833 km. Each channel is also sensitive to radiation of a particular polarisation as defined in Table 1, the direction of which rotates with scan angle. The differences in the polarisation for Channels 3 and 4 on MHS compared
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2. Functional description humidity sounders
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summer. This is consistent with the results of Melsheimer and Heygster [2008]. So for all channels on microwave humidity sounders, there is a significant contribution from the Antarctic surface and the Arctic surface in winter, and the radiation which reaches the satellite is then determined substantially by the surface skin temperature and the surface emissivity: the atmospheric contribution is relatively small. High-latitude surfaces are highly inhomogeneous, consisting of land, water, ice, or snow whose emissivities are significantly different [Weng et al., 2001; Weng and Yan, 2004]. Land surfaces have an emissivity close to 0.95 (note that surfaces with snow or sand have lower emissivity at these frequencies); ocean emissivity varies considerably depending on oceanic characteristics including surface roughness which is influenced by overlying atmospheric conditions; and snow and sea-ice emissivity also varies considerably [Mathew et al., 2008]. Therefore measures are necessary to reduce the noise related to surface inhomogeneity. Furthermore, near-polar SNOs only sample brightness temperatures which are not representative of lower latitudes. Owing to non-linearity in the calibration, error in warm target measurements, and obstructed space view, inter-satellite biases can vary with scene-radiance [e.g., Zou et al., 2006]. Therefore, there are several reasons why near-polar SNOs are inadequate for inter-calibrating the microwave humidity sounders. Owing to atmospheric drag, the Earth’s non-sphericity, and gravitational pull from celestial bodies the orbit of a polar orbiting satellite drifts and its local equator crossing time changes. When the equator crossing times of a pair of satellites become nearly the same, SNOs can occur at all latitudes for a short period, typically one or two months. We use these SNOs at all latitudes to estimate the adequacy of polar SNOs to inter-calibrate microwave humidity sounders. Section 2 gives a short technical description of the humidity sounders and their channel characteristics. Section 3 revisits a recent comparison between simulated AMSU-B and MHS to show that global SNOs are necessary for reliable inter-calibration. Section 4 describes the data and methods of analysis. Section 5 presents the results and Section 6 provides a summary and conclusions.
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Figure 2. Left panels show simulated brightness temperature differences between MHS and AMSU-B as a function of precipitable water vapor for (top) Channel 2 and (bottom) Channel 5 using a diverse atmospheric profile data set compiled from ECMWF forecasts [Chevallier et al., 2006]. Profiles are separated for ocean and land. Ocean emissivity is 0.6, land emissivity is 0.95 and emissivity of mixed grid point profiles varies linearly between 0.6 and 0.95. Right panels shows simulated brightness temperature differences as a function of mean brightness temperatures of AMSU-B and MHS. Note the simulations are only for nadir.
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3. Comparison of simulated AMSU-B and MHS measurements Kleespies and Watts [2007] compared the brightness temperatures simulated for MHS and AMSU-B using the 48 profiles of Strow et al. [2003]. Significant differences were found only for Channels 2 and 5 and in both cases mean MHS brightness temperatures were colder than those of AMSU-B. We revisit the study to investigate the dependence of bias between the two instruments for surface and atmospheric conditions, enabling us to interpret the results of our SNO analysis for these channels. Figure 2 shows simulated brightness temperature differences between MHS and AMSU-B using 5000 diverse profiles, sampled from ECMWF forecasts to span the natural variability of the real atmosphere [Chevallier et al., 2006]. The simulations used a line-by-line radiative transfer model [Buehler et al., 2005a] that was already used in a number of inter-comparison studies [Buehler et al., 2004; John and Buehler , 2005; Moradi et al., 2010]. Surface emissivity at these frequencies varies considerably with surface type, with higher emissivity for land (∼0.95) and lower emissivity for ocean (∼0.6). Therefore in the simulations we used an emissivity of 0.95 for land profiles and 0.6 for ocean profiles. For profiles from a model grid box which has both land and sea we calculated the emissivity based on land cover linearly varying between 0.6 and 0.95. Results are shown only for Channels 2 and 5 because for the other three channels the differences are negligibly small. The differences are shown as functions of brightness temperature (right panels) and precipitable water vapor (PWV, left panels) which is the vertically integrated water vapor density. The top panel shows the differences for Channel 2 which is at 150 GHz on AMSU-B but at 157 GHz on MHS. Channel 2 is a sounding channel in a humid atmosphere, but with a surface contribution which increases as atmospheric moisture decreases. With a very moist atmosphere, the surface has little effect and the brightness temperature of MHS is lower than that of AMSU-B, because the atmosphere is slightly more opaque at 157 GHz than at 150 GHz (see Figure 1), raising the sounding altitude slightly. With a less moist atmosphere, the higher atmospheric opacity at 157 GHz than at 150 GHz makes the radiometrically cold surface have less influence on MHS than on AMSU-B, leading to higher brightness temperature for MHS. This is especially true for the ocean (blue symbols in Figure 2) because of its lower emissivity. When there is very little water vapor, the difference is close to zero because both instruments sample the surface which has a similar emissivity at 150 and 157 GHz. It is clear from the figure that the differences can have a wide range from −2 to 7 K depending on atmospheric and surface conditions (Kleespies and Watts [2007] reported −1.54±2.03 K bias) and thus it is not straightforward to combine AMSU-B and MHS Channel 2 radiances by adding an offset to one of the measurements. The bottom panel shows the brightness temperature difference for Channel 5. As for Channel 2, there is little difference when the atmosphere is almost free of water vapor and it starts increasing with water vapor. When precipitable water is around 3 mm the trade off between surface and sounding channel effects come into play and the difference starts to decrease. When there is about 15 mm of precipitable water the channel becomes a sounding channel and insensitive to surface. MHS Channel 5 is measuring colder radiances compared to the AMSU-B one, which is
about −0.6 K irrespective of surface type in an atmosphere with 20 mm or more precipitable water vapor. The right panels in Figure 2 show simulated brightness temperature differences for Channels 2 and 5 as a function of average scene brightness temperatures of AMSU-B and MHS. Transition from surface to sounding channel is clearly seen for sea points due to radiometrically colder surface which amplifies the water vapour signal from the atmosphere. Although it is possible to combine AMSU-B and MHS data for Channel 5 [Kleespies and Watts, 2007] by adding a global offset to account for the frequency changes, the systematic major variations in bias between a dry polar atmosphere and a moist lower-latitude atmosphere lead us to conclude that biases from these channels estimated from polar SNOs cannot represent humid lower latitudes.
4. Collocation and analysis methods We used the collocation method based on Holl et al. [2010] (some details given in Appendix A). Sensitivity of distance and time thresholds for selecting collocations to the uncertainty in the estimated bias is shown in Figure 4. Consequently, to overcome spatial inhomogeneity we used only those pixel pairs whose centres are closer than 5 km, which is less than one third of the 16.3 km pixel diameter at nadir. We discard any measurements with time differences exceeding 300 seconds, to avoid changes in scene properties such as clouds. We used only 4 pixels each on either side of nadir, to avoid errors arising from limb effects and scan asymmetry. This also minimises the impact of polarisation differences. Collocations over both land and ocean are used throughout this study. Using those pixel pairs which satisfied these stringent criteria, we first calculated differences in brightness temperatures and then derived the mean difference or bias (ΔTB ) and the standard deviation of the differences (σΔTB ). The standard deviation of collocated brightness temperatures (or in other words, SNO variability) has mainly two sources [Iacovazzi and Cao, 2008]: one is the combined radiometric noise (NEΔT, which is the smallest change in input brightness temperature that can be detected in the system output (i.e. calibrated brightness temperatures, including contributions from calibration noise))of the two instruments and the other is the scene (spatial and temporal) inhomogeneity. In order to have robust statistics, we collected data for a month to calculate ΔTB and σΔTB . This is an advance over previous studies which consider individual SNO events which have fewer pixel pairs for computing statistics. We also calculate standard errors of mean values, namely σΔTB divided by the square root of the number of collocations. Clouds affect these channels [Sreerekha et al., 2008], but we have not screened for them. This is mainly because in polar conditions it is difficult to differentiate between clouds and the surface. Due to our stringent spatio-temporal collocation criteria, we assume that measurements from both instruments are affected by clouds in a similar way.
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Figure 4. Sensitivity test to select distance and time threshold for collocations. Standard deviation of brightness temperature difference in Kelvin for each grid box is shown. Distance grid is equally spaced with 1 km distance, but time grid has variable width. We have randomly selected 120 points from each grid box to calculate statistics. Grid boxes in white have too few collocations to make statistics. Collocations are taken from 70–80◦ latitudes in both hemispheres of MA–N17 collocations.
5. Results 5.1. Selection of SNOs Figure 3 shows the equator crossing times of the ascending nodes [Ignatov et al., 2004] of NOAA and MetOp polarorbiting satellites. The orbital parameters of these satellites are designed so that equator crossing time will drift away from local noon, because if a satellite crosses the equator at noon, this can affect the functioning of both the satellite and the instruments on-board owing to different solar illumination. The drift creates the possibility that satellite pairs will have similar equator crossing times for short periods.
During these time periods SNOs can occur globally. We have discovered that in recent years there have been SNOs at all latitudes and this is to our knowledge the first study to exploit this. We have identified 4 months of data with sufficient number of collocations satisfying our stringent criteria (Δx less than 5 km and Δt less than 300 sec) at all latitudes. They are: 2008-08 for the N16-N15 pair, 2009-04 and 2009-05 for the MA-N17, and 2009-09 for the N19-N18. We assign newer platforms NOAA-16, MetOpA, and NOAA-19 as primary satellites and NOAA-15, NOAA-17, and NOAA-18 as secondary satellites. Bias is calculated as primary satellite minus secondary satellite. We partitioned the collocations into eighteen 10◦ latitude bins. The top panel in Figure 9 shows the latitudinal distri-
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Figure 5. Mean and standard deviation of brightness temperature for latitude bins. Only those collocations with centre of pixels less than 5 km apart and measurement time difference less than 300 s are used to compute statistics. The width of latitude bins is 10 degrees. First row: NOAA-19 and NOAA18, 2009-09. Second and third rows: MetOpA and NOAA-17 during 2009-05 and 2009-04, respectively. Fourth row: NOAA-15 and NOAA-16, 2008-08. bution of the number of collocations. The number of collocations varies for each satellite pair, with the N19-N18 pair having the most, about 50000-100000, collocations in each latitude bin. Most of the bins have 5000 or more collocations which are enough collocations to compute robust statistics. 5.2. Interpretation of SNOs Biases are expected to vary with scene-radiance (Section 3), so estimates of biases derived from SNOs at all latitudes will be particularly valuable if they vary systematically with latitude. On the other hand, the estimates will be less useful if they are noisy. So before presenting our main results we consider these two aspects. 5.2.1. Meridional distribution of brightness temperature In order to interpret the meridional distribution of biases in the measurements, we need to know the meridional distribution of the brightness temperatures. Figure 5 shows the mean and standard deviation of brightness temperatures for each latitude bin for each channel. A common feature is the very low brightness temperatures south of 70◦ S. Variability is greater over these southern polar regions because the heterogeneous surface conditions show through the very dry atmosphere. Channel 1 is a surface channel at all latitudes: as seen in Figure 1, the total opacity is less than one even for the very wet profile. Accordingly it also shows low brightness temperatures for the mid-latitude southern hemisphere and for the Arctic, as does Channel 2 for the same reason. This might be associated with less land mass in these lati-
tudes and lower ocean emissivity. Because of its sensitivity to the surface, Channel 1 also has high variability. 5.2.2. Uncertainties in SNO method An important source of uncertainty for the SNO method is the radiometric noise of the instruments [Iacovazzi and Cao, 2008]. This is normally expressed as noise equivalent brightness temperature (NEΔT): the first flight model values taken from Goodrum et al. [2007] for each channel are given in Table 1. NEΔT is time varying, it generally increases as the instrument starts to degrade. It can also increase due to a change in the operating conditions of the satellite and due to radio frequency interference (RFI) from nearby transmitters or other instruments. Mean NEΔT values for the analysis time period for all the channels are given in Table 2. NEΔT were determined from the warm target views during the analysis time period. Note for N19 Channel 3 the noise was about 2.5 K for the first half of September 2009, but more than 7 K for the second half of the month. Note the performance of this channel became better by the beginning of 2011. Scene inhomogeneity is another source of uncertainty in the SNO method owing to spatial and temporal mismatches in collocated pixels. Figure 6 shows standard deviations of brightness temperature differences reflecting these uncertainties. Horizontal lines indicate the combined instrument noise based on values given in Table 2. Channel 1 shows standard deviations from 1 to 2 K which are higher than the combined instrument noise. For Channel 2, N16–N15 (both having AMSU-B) and N19–N18 (both having MHS) show standard deviations from 1 to 1.5 K, approximately consistent with the specified NEΔT of these instruments. The
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Figure 6. Standard deviation of the brightness temperature differences (σΔTB ). Black circles: NOAA16–NOAA-15 during 2008-08, green and blue circles: MetOpA–NOAA-17 during 2009-04 and 2009-05, respectively and the red circles: NOAA19–NOAA18 during 2009-09. Horizontal lines indicate the combined instrument noise based on values given in Table 2. MA–N17 pair (MA has MHS and N17 has AMSU-B) has higher standard deviation which can be explained by the differences between 150 and 157 GHz emissions for very different surface emissivities (land and sea) north of 40◦ S (see discussions in Section 3). Channel 3 shows different standard deviations for different satellite pairs. If NEΔT accords with pre-launch specifications (Table 1), we would expect the effective variability associated with NEΔT to be equivalent to 1.5 K for the AMSU-B–AMSU-B √ combination, 1.18 K for the AMSU-B– MHS combination ( 1.062 + 0.512 = 1.18 K), and 0.7 K for the MHS–MHS combination. The MA-N17 pair comparing AMSU-B and MHS shows SNO variability close to instrument specification: even at high latitudes, where the surface is highly variable, standard deviations remain small. Thus there is very little contribution from scene inhomogeneity, given our stringent collocation criteria. The other two satellite pairs show significantly higher variability than expected from pre-launch instrument specifications. N19–N18 has the highest value of about 9 K, owing to known instrument problems causing exceptionally high noise in Channel 3 on N19 at the time of the comparison. N16–N15 has about 4 K standard deviation which is also much higher than the specified noise of the instruments. Our analysis (Table 2) indicates that for both N16 and N15 the NEΔT have increased due to instrument problems. Channels 4 and 5 also show standard deviations consistent with NEΔT of the instruments, except for the N16–N15 pair which shows inflated standard deviations owing to instrument degradation (Table 2). The standard deviations are invariant with latitude for these channels as well which leads to the conclusion that there is little infuence by scene inhomogeneity in the estimated bias, given our stringent collocation criteria. 5.3. Meridional distribution of bias Figure 7 shows the bias and its standard error for all latitude bins and for all satellite pairs. Inter-satellite bias is time varying, so the results shown here represent only the time period analysed. 5.3.1. Channel 1 (89 GHz) Channel 1 shows very small inter-satellite biases. N16 is about 0.15 K warmer than N15 for most latitude bins. MA
measurements are also warmer than N17 measurements by about 0.2 K, but with a few outliers. Though N19–N18 bias is small there is a latitude dependence, with negative bias for high latitudes and positive bias for low latitudes. 5.3.2. Channel 2 (150/157 GHz) N16-N15 bias is very stable across all latitudes at about 0.5 K except for the two southern most latitude bins. N19– N18 bias is clearly latitude-dependent, being as low as −0.3 K at high southern latitudes and 0.1 K at low latitudes, with a pattern similar to Channel 1. The MA-N17 pair (AMSU-B and MHS combination) shows large biases, up to 4 K and high variability in bias with latitude, as expected from our analysis of simulated brightness temperatures for this channel in Section 3. Biases are consistent for April and May 2009. 5.3.3. Channel 3 (183.31±1.00 GHz) N16-N15 shows the largest biases, ranging from 1 to 2 K with a latitude dependence: 1.8 K bias near the South Pole which decreases to 1 K near the North Pole. N19–N18 has biases ranging from −0.2 to 0.6 K with no obvious latitude dependence, but with large standard error. Note that N19 had exceptionally high noise for this Channel. MA-N17 biases vary between −0.15 K to 0.4 K, being positive at high latitudes and near-zero or negative at low latitudes. 5.3.4. Channel 4 (183.31±3.00 GHz) N16-N15 has significant intersatellite bias which varies linearly from 4 K at the South Pole to near zero at the North Pole. N19–N18 biases are close to 0.2 K at low latitudes and the biases vary considerably with latitude. MA–N17 also show latitude dependence with high latitudes showing positive biases up to 0.5 K whereas at low latitudes the biases are very slightly negative. 5.3.5. Channel 5 (183.31±7.00/+7.00 GHz) N16–N15 biases also vary linearly with latitude for Channel 5, from −3 K near the South Pole to −5.5 K near the North Pole. N19–N18 biases are close to zero except for the two southernmost latitude bins where the bias is close to −0.3 K. MA-N17 has the AMSU-B–MHS combination and this channel on MHS has only the upper sideband, so larger biases are expected. The biases show strong latitude dependence: positive at higher latitudes and near-zero or negative at lower latitudes.
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Figure 7. Black circles and vertical bars show bias (ΔTB ) for latitude bins and its standard error estimated using SNOs. First row: NOAA-19–NOAA-18 during 2009-09. Second and third row: MetOpA– NOAA-17 during 2009-05 and 2009-04, respectively. Fourth row: NOAA-16–NOAA-15 for 2008-08. Red circles show bias estimated from zonal mean brightness temperatures (see Section 5.3.6 for details). Note that some of the red circles out of the plot range. It is interesting to note that bias patterns are broadly similar for Channels 3, 4, and 5 for AMSU-B and for Channels 3 and 4 for MHS. This similarity might be manifested by common local oscillator and mixer used by these channels. 5.3.6. Consistency check on estimated bias As an independent estimate to check the bias obtained from SNO method, biases were also calculated using zonal averaged brightness temperatures. This method was already used by Shi and Bates [2011] for infrared channels. We used only near-nadir brightness temperatures to avoid scanbias/limb-effect. This method works well when the sampling times of two satellites are similar which is the case of our analysis. If sampling times were different, differences would arise from the diurnal cycles of humidity and temperature [Zou et al., 2006]. Biases are calculated for 18 latitude bins as in our SNO analysis. Red circles in Figure 7 shows the estimated biases using this method. This method works well in general except for Channel 1 due to very small biases for this channel. Thus, it is confirmed that the latitude dependence of bias estimated using SNO method is correct and polar SNOs alone cannot be used to estimate inter-satellite biases. Though, the zonal average brightness temperature method is found to be useful for the analysed time period,
it is not certain whether it will work for other time periods due to differences in temporal sampling of the satellites and we are currently investigating this. 5.4. Dependence of bias on scene-radiance Inter-satellite bias can vary with scene-radiance, TB [e.g., Shi et al., 2008]. Therefore in Figure 8 we show biases and their standard errors estimated from global SNOs as a function of TB of each satellite. We did not average TB s across a satellite pair, because the dependence of bias on TB can vary between satellites. Blue circles in the figure show dependence of bias as a function of TB measured by primary satellites (N16, MA, and N19) and green circles do likewise but with reference to secondary satellites (N15, N17, and N18). We have collated biases into 10 K brightness temperature bins and then computed their mean and standard error for all bins with 100 or more data values. 5.4.1. Channel 1 N16–N15 bias tends to decrease with increasing sceneradiance for N15, but not for N16. MA–N17 biases also tend to decrease with N17 TB but increase with MA TB s. N19–N18 shows a strong increase in bias with both TB . 5.4.2. Channel 2 For both N16–N15 and and N19–N18 biases generally increase with TB of the primary satellites. MA-N17 has peak biases at a TB of about 250 K for either satellite which is ex-
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Figure 8. Blue circles show bias (ΔTB ) as a function of brightness temperature of primary satellites and the green circles show bias as a function of brightness temperature of secondary satellites and the vertical bars show standard errors of the biases. Primary satellites are N16, MA, and N19. Secondary satellites are N15, N17, and N18. First row: NOAA-19–NOAA-18 during 2009-09. Second and third row: MetOpA–NOAA-17 during 2009-05 and 2009-04, respectively. Fourth row: NOAA-16–NOAA-15 for 2008-08. actly what is expected based on our discussion in Section 3 using simulated radiances (see Figure 2). 5.4.3. Channel 3 For Channel 3, N19–N18 bias varies with N19 TB s, from about −20 K at 160 K to 45 K at 310 K. This clearly indicates the instrument problem for this channel. This apparent large bias can be explained by the large noise of N19. The range of brightness temperature is larger for N19 due to higher noise. This in turn will lead to a negative bias for colder N19 TB bins and to a positive bias for warmer N19 TB bins. N16-N15 bias also shows dependence on TB s of both satellites. The bias starts increasing with N16 TB s and then stays constant from 170 K to 230 K and then dips before increasing again. Note that TB s below 230 K are mostly from the two southernmost bins where the channel is a window channel. The bias varies from about −2 K to 6 K with N16 TB s above 230 K. Bias seems to decrease with N15 TB s (3 K to −1 K), so the overall bias is reduced due to contrasting bias dependence on N15 and N16 TB s. MA–N17 biases generally decrease with both Tbs. 5.4.4. Channel 4 Channel 4 bias patterns are similar to those of Channel 3 for MA–N17. N19–N18 bias increases with N19 TB s but does not show any clear relationship with N18 TB s. N16– N15 bias stays constant with both TB s blow 240 K and then starts to decrease up to 260 K. The bias then starts to in-
crease with N15 TB s but continues to decrease with N16 TB s. 5.4.5. Channel 5 Channel 5 on N19–N18 shows a strong increase in bias with both TB s: −0.5 K at 160 K and increasing to 0.1 K at 300 K. MA–N17 pair shows larger biases due to the frequency difference as discussed in Section 3 with biases increasing with TB s and then starts decreasing when the channel becomes a sounding channel. N16–N15 biases show a very strong dependence on N15 TB s; −6 K at 250 K and 0.5 K at 300 K. 5.4.6. Explaining latitude dependence of bias The latitude dependence of inter-satellite biases can be explained by their dependence on scene-radiance. For example, the N19–N18 pair shows rather monotonically increasing bias with increasing TB s for all channels. This leads to similar meridional distribution of TB s and bias, except for Channel 3 due to the large noise of N19. Another example is Channels 3–5 of MA–N17 which show decreasing bias with increasing TB s, and thus shows opposite meredional patterns for bias and TB s.
6. Summary and conclusions Cao et al. [2004, 2005] have shown that the simultaneous nadir overpass (SNO) method is useful for inter-calibrating
89 JOHN ET AL.: SNOS AND INTER-CALIBRATION OF HUMIDITY SOUNDERS
Figure 9. Number of collocations in 10◦ latitude bins. Each collocation satisfies stringent spatio-temporal crieteria (Δx < 5 km and Δt < 300 sec). Black circles show collocations of NOAA-15 and NOAA-16 during 200808, green and blue circles show collocations of MetOpA and NOAA-17 during 2009-04 and 2009-05, respectively and red circles show the collocations of NOAA19 and NOAA18 during 2009-09. Note the logarithmic y-axis scale. Map plots show geographical distribution of SNOs. satellite instruments. Nevertheless, [Iacovazzi and Cao, 2008] expressed concerns over using SNOs for surface sensitive channels. Owing to their normal occurrence in the polar regions, SNOs have potential problems for their use in inter-calibrating microwave humidity sounding channels which are surface sensitive under dry polar atmospheric conditions. But as a result of orbital drift, SNOs can occur globally for a short period of time for polar orbiting satellite pairs when their local equator crossing times become close. We used these global SNOs to evaluate inter-calibration using only polar SNOs. There are 3 satellite pairs with global SNOs for microwave humidity sounders. They are NOAA-16(N16)– NOAA15(N15) during 2008-08, MetOpA(MA)–NOAA17(N17) during 2009-04 and 2009-05, and NOAA-19(N19)– NOAA-18(N18) during 2009-09. N15, N16, and N17 have the Advanced Microwave Sounding Unit-B (AMSU-B) and N18, N19, and MA have the Microwave Humidity Sounder (MHS). We have shown using simulated brightness tempertures that the differences for these channels between AMSUB and MHS are dependent on the amount of water vapor in the atmosphere and on the scene-radiance. The differences for Channel 2 ranges between −2 to 7 K and for Channel 5 from −1 to 3 K, but for other channels the differences are negligible.. The method used to obtain collocations is based on Holl et al. [2010]. We used only those collocations with spatial differences less than 5 km and temporal differences less than 300 seconds, based on sensitivity analyses, to avoid uncertainties due to scene inhomogeneities. We then partitioned the collocated measurements into eighteen 10◦ bins. All channels show a large range (∼100 K) in brightness temperature across the latitudes with coldest brightness temperature
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near the South Pole and the warmest in the tropics. The main source of uncertainty in the SNO method is the combined radiometric noise of the instrument pair. The standard deviations of brightness temperature differences are invariant with latitude indicating that scene inhomogeneities play only a minimal role, given our stringent collocation criteria. The sounding channels (Channels 3–5) show different values of standard deviations across the satellite pairs which is consistent with their radiometric noise. For example, the largest standard deviation of about 9 K is shown by N19– N18 pair for Channel 3 owing to the anomalously large noise of N19. Channel 1 generally shows small inter-satellite biases and less latitude dependence compared to other channels. Channel 2 has higher bias (up to 3.5 K) for the AMSU-B–MHS combination which is consistent with the results based on simulated radiances shown in Section 3. N19–N18 shows a strong latitude dependence for biases in Channel 2. N16– N15 shows the largest biases for Channels 3, 4, and 5 and also shows a strong latitude dependence. We have validated the biases estimated from global SNOs by biases estimated from zonal mean near-nadir brightness temperatures. We suggest that it is not appropriate to use SNOs over a restricted latitude range to inter-calibrate humidity sounders. The reason for the latitude dependence of biases primarily originates from their dependence on scene-radiance which themselves have a latitude dependence. It was shown that the dependence of biases on one satellite could be different from another. Channel 3 of N16–N15 shows this behaviour with biases increasing with N16 brightness temperatures and decreasing with N15 brightness temperatures. We suggest that it is important to take into account the dependence of biases on scene- radiance during the inter-calibration procedure. It has to be kept in mind that the present study explores the global SNOs which are available only for a short time during the life of satellites, thus cannot be used to estimate temporal evolution of bias [e.g., Zou et al., 2006]. Another method for inter-calibration that is being developed is monitoring of satellite radiometer biases using NWP fields [Saunders et al., 20xx] which allows global sampling during the entire life time of the satellites. Our plan is to combine the SNO method with the the NWP method to inter-calibrate microwave humidity sounders. This work is being done as part of a project to homogenise radiances measured by microwave humidity sounders. The next step is to include SSM/T-2 data as well in our analyses. Inter-satellite biases are generally estimated using only near-nadir radiances. To apply these bias estimates to measurements at other viewing angles requires that there is no scan dependent biases, but in reality there is scan-dependent biases [e.g., Buehler et al., 2005b]. These asymmetries will also be estimated as part of this project.
Appendix A: collocation methodology We used the collocation code from Holl et al. [2010]. This code is designed for any pair of satellite sensors and not specifically designed for the study performed here. However, the selection of data fulfilling spatial criteria was modified to improve performance, and is different from the algorithm described in Holl et al. [2010]. The first steps are the same: orbits with temporal overlap are located, and then the segments within those pairs of orbits that have a time overlap (+/- the maximum time for a collocation) are located. This is described in detail in Holl et al. [2010]. In this study, all individual measurements are binned according to their latitude/longitude-values, resulting in two “gridded” datasets for this orbital segment. For all grid cells where one
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sensor has measurements and the other sensor has measurements in the same or a nearby grid cell, all time differences between measurements from the one and the other sensor are calculated. Here, ”nearby” is a function of cell size and maximum collocation distance. The number of neighbouring cells to explore for collocations is chosen such that no collocations can be missed. For example, if the maximum collocation distance is 15 km and cells are 1◦ ×1◦ , a cell at 85◦ N is only 9.7 km wide (note that most satellites do not reach so close to the pole). In order not to miss any collocations, this means that measurements from a cell centering at (0◦ , 85◦ N) are compared to all measurements in the fifteen cells spanning from (2◦ W, 86◦ N) to (2◦ E, 84◦ N). However, measurements from a cell at (0, 45N), where the cell is 79 km wide, need to be compared only within the nine cells spanning from (1◦ W, 46◦ N) to (1◦ E, 44◦ N). If this spatial criterion is also met, the collocation is selected for further processing. Acknowledgments. We thank three anonymous reviewers, Richard Allan, and John Eyre, Nigel Atkinson, Marc Shroeder, and Joerg Shulz for valuable comments. Viju John and David Parker were supported by the Joint DECC/Defra Met Office Hadley Centre Climate Programme (GA01101) and Viju John was also supported by the UK JWCRP. This work contributes to COST Action ES604–Water Vapor in the Climate System (WaVaCS). Thanks to Lisa Neclos of the NOAA CLASS for AMSU-B and MHS Level-1b data, EUMETSAT NWP-SAF for the AAPP software to process the data, and ARTS community for their radiative transfer model.
References Andersson, E., E. Holm, P. Bauer, A. Beljaars, G. A. Kelly, A. P. McNally, A. J. Simmoons, J.-N. Thpaut, and A. M. Tompkins (2007), Analysis and forecast impact of the main humidity observing systems, Q. J. R. Meteorol. Soc., 133, 1473–1485, doi:10.1002/qj.112. Bonsignori, R. (2007), The Microwave Humidity Sounder (MHS): in-orbit performance assessment”, in Proc. SPIE, 67440A, vol. 6744, doi:10.1117/12.737986. Buehler, S. A., M. Kuvatov, V. O. John, U. Leiterer, and H. Dier (2004), Comparison of microwave satellite humidity data and radiosonde profiles: A case study, J. Geophys. Res., 109, D13103, doi:10.1029/2004JD004605. Buehler, S. A., P. Eriksson, T. Kuhn, A. von Engeln, and C. Verdes (2005a), ARTS, the atmospheric radiative transfer simulator, J. Quant. Spectrosc. Radiat. Transfer, 91 (1), 65–93, doi:10.1016/j.jqsrt.2004.05.051. Buehler, S. A., M. Kuvatov, and V. O. John (2005b), Scan asymmetries in AMSU-B data, Geophys. Res. Lett., 32, L24810, doi:10.1029/2005GL024747. Buehler, S. A., M. Kuvatov, V. O. John, M. Milz, B. J. Soden, D. L. Jackson, and J. Notholt (2008), An upper tropospheric humidity data set from operational satellite microwave data, J. Geophys. Res., 113, D14110, doi:10.1029/2007JD009314. Cao, C., M. Weinreb, and H. Xu (2004), Predicting simultaneous nadir overpasses among polar-orbiting meterological satellites for the intersatellite calibration of radiometers, J. Atmos. Oceanic Technol., 21, 537–542. Cao, C., H. Xu, J. Sullivan, L. McMillin, P. Ciren, and Y. Hou (2005), Intersatellite radiance biases for the High Resolution Infrared Radiation Sounders (HIRS) onboard NOAA-15, 16, and -17 from simultaneous nadir observations, J. Atmos. Oceanic Technol., 22 (4), 381–395. Chevallier, F., S. Di Michele, and A. P. McNally (2006), Diverse profile datasets from the ECMWF 91-level short-range forecasts, Tech. rep., NWP SAF Satellite Application Facility for Numerical Weather Prediction, document No. NWPSAF-ECTR-010, Version 1.0. Chung, E.-S., B. J. Soden, B.-J. Sohn, and J. Schmetz (2011), Model-simulated humidity bias in the upper troposphere and its relation to the large-scale circulation, J. Geophys. Res., doi:10.1029/2011JD015609, in press.
Dee, D. P., et al. (2011), The ERA-Interim reanalysis: configuration and performance of the data assimilation system, Quarterly Journal of the Royal Meteorological Society, 137 (656), 553–597, doi:10.1002/qj.828. Eymard, L., F. Karbou, S. Janicot, N. Chouaib, and F. Pinsard (2010), On the use of Advanced Microwave Sounding Unit-A and -B measurements for studying the monsoon variability over West Africa, J. Geophys. Res., 115, D20115, doi: 10.1029/2009JD012935. Goldberg, M., et al. (2011), The global space-based intercalibration system, Bulletin of the American Meteorological Society, 92 (4), 467–475, doi:10.1175/2010BAMS2967.1. Goodrum, G., K. B. Kidwell, and W. Winston (2007), NOAA KLM user’s guide, Tech. rep., National Environmental Satellite, Data, and Information Services (NESDIS). Holl, G., S. A. Buehler, B. Rydberg, and C. Jim´enez (2010), Collocating satellite-based radar and radiometer measurements – methodology and usage examples, Atmos. Meas. Tech., 3 (3), 693–708, doi:10.5194/amt-3-693-2010. Iacovazzi, R. A., and C. Cao (2007), Quantifying EOS aqua and NOAA POES AMSU-A brightness temperature biases for weather and climate applications utilizing the SNO method, J. Atmos. Oceanic Technol., 24, 1895–1909, doi:10.1175/ JTECH2095.1. Iacovazzi, R. A., and C. Cao (2008), Reducing uncertainties of SNO-estimated inter-satellite AMSU-A brightness temperature biases for surface-sensitive channels, J. Atmos. Oceanic Technol., 25, 1048–1054. Ignatov, A., I. Laszlo, E. D. Harrod, K. B. Kidwell, and G. P. Goodrum (2004), Equator crossing times for noaa, ers and eos sun-synchronoussatellites, Int. J. Remote Sensing, 25 (23), 5255–5266. John, V. O., and S. A. Buehler (2004), The impact of ozone lines on AMSU-B radiances, Geophys. Res. Lett., 31, L21108, doi: 10.1029/2004GL021214. John, V. O., and S. A. Buehler (2005), Comparison of microwave satellite humidity data and radiosonde profiles: A survey of European stations, Atmos. Chem. Phys., 5, 1843–1853, doi:10.5194/acp-5-1843-2005, sRef-ID:1680-7324/acp/2005-51843. John, V. O., and B. J. Soden (2007), Temperature and humidity biases in global climate models and their impact on climate feedbacks, Geophys. Res. Lett., 34, L18704, doi:10.1029/ 2007GL030429. John, V. O., G. Holl, R. P. Allan, S. A. Buehler, D. E. Parker, and B. J. Soden (2011), Clear-sky biases in satellite infra-red estimates of upper tropospheric humidity and its trends, J. Geophys. Res., 116, D14108, doi:10.1029/2010JD015355. Kleespies, T. J., and P. Watts (2007), Comparison of simulated radiances, jacobians and linear error analysis for the Microwave Humidity Sounder and the Advanced Microwave Sounding Unit-B, Q. J. R. Meteorol. Soc., 132, 3001–3010. Mathew, N., G. Heygster, C. Melsheimer, and L. Kaleschke (2008), Surface emissivity of polar regions at amsu window frequencies, IEEE T. Geosci. Remote, 46 (8), 2298–2306, doi: doi:10.1109/TGRS.2008.916630. Melsheimer, C., and G. Heygster (2008), Improved retrieval of total water vapor over polar regions from AMSU-B microwave radiometer data, IEEE T. Geosci. Remote, 46 (8), 2307–2322, doi:doi:10.1109/TGRS.2008.918013. Miao, J., K. Kunzi, G. Heygster, T. Lachlan-Cope, and J. Turner (2001), Atmospheric water vapor over Antarctica derived from Special Sensor Microwave/Temperature 2 data, J. Geophys. Res., 106 (D10), 10,187–10,203. Moradi, I., S. A. Buehler, V. O. John, and S. Eliasson (2010), Comparing upper tropospheric humidity data from microwave satellite instruments and tropical radiosondes, J. Geophys. Res., 115, D24310, doi:10.1029/2010JD013962. Petty, G. W. (2006), A first course in atmospheric radiation, Sundog Publishing. Saunders, R. W., T. J. Hewison, S. J. Stringer, and N. C. Atkinson (1995), The radiometric characterization of AMSUB, IEEE T. Microw. Theory, 43 (4), 760–771. Saunders, R. W., B. Candy, P. N. Francis, T. Blackmore, and T. Hewison (20xx), Monitoring satellite radiometer biases using NWP fields, TBD, to be submitted. Seidel, D. J., et al. (2009), Reference upper-air observations for climate: Rationale, progress, and plans, Bull. Amer. Met. Soc., 90 (3), 361–369, doi:10.1175/2008BAMS2540.1.
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of an ongoing controversy, Wiley Interdisciplinary Reviews: Selbach, N., T. J. Hewison, G. Heygster, J. Miao, A. J. McGrath, and J. P. Taylor (2001), Validation of total water vapor reClimate Change, published Online: Nov 15 2010. trieval with an airborne millimeter-wave radiometer over arctic Wang, L., C. Cao, and P. Ciren (2007), Assessing noaa-16 hirs sea ice, Tech. rep., xxxx. radiance accuracy using simultaneous nadir overpass observaShi, L., and J. J. Bates (2011), Three decades of intersatellitetions from airs, J. Atmos. Oceanic Technol., 24, 1546–1561, calibrated High-Resolution Infrared Radiation Sounder upper doi:10.1175/JTECH2073.1. tropospheric water vapor, J. Geophys. Res., 116, D04108, doi: Weng, F., and B. Yan (2004), A microwave snow emissivity 10.1029/2010JD014847. model, in The Technical Proceedings of The Thirteenth InShi, L., J. J. Bates, and C. Y. Cao (2008), Scene radianceternational TOVS Study Conference (ITSC XIII), St Adele, dependent intersatellite biases of hirs longwave channels, J. Canada. Atmos. Oceanic Technol., 25 (12), 2219–2229, doi:10.1175/ Weng, F., B. Yan, and N. C. Grody (2001), A microwave land 2008JTECHA1058.1. emissivity model, J. Geophys. Res., 106 (D17), 20,115–20,123. Sohn, B. J., E. S. Chung, J. Schmetz, and E. A. Smith (2003), EsXavier, P. K., V. O. John, S. A. Buehler, R. S. Ajayamohan, and timating upper-tropospheric water vapor from SSM/T-2 satelS. Sijikumar (2010), Variability of indian summer monsoon in lite measurements, J. Appl. Meteorol., 42 (4), 488–504, doi: a new upper tropospheric humidity data set, Geophys. Res. 10.1175/1520-0450(2003)0420488:EUTWVF2.0.CO;2. Lett., 37, L05705, doi:10.1029/2009GL041861. Sreerekha, T. R., S. A. Buehler, U. O’Keeffe, A. Doherty, C. Emde, and V. O. John (2008), A strong ice cloud event as Zou, C.-Z., M. D. Goldberg, Z. Cheng, N. C. Grody, J. T. seen by a microwave satellite sensor: Simulations and obserSullivan, and D. Tarpley (2006), Recalibration of microwave vations, J. Quant. Spectrosc. Radiat. Transfer, 109 (9), 1705– sounding unit for climate studies using simultaneous nadir 1718, doi:10.1016/j.jqsrt.2007.12.023. overpasses, J. Geophys. Res., 111 (D19114), doi:10.1029/ Strow, L. L., S. E. Hannon, S. D. Souza-Machado, H. E. Mot2005JD006798. teler, and D. Tobin (2003), An overview of the AIRS radiative transfer model, IEEE T. Geosci. Remote, 41 (2), 303–313. Viju Oommen John, Met Office Hadley Centre, Exeter, UK, Thorne, P. W., J. R. Lanzante, T. C. Peterson, D. J. Seidel, and (viju.john@metoffice.gov.uk) K. P. Shine (2010), Tropospheric temperature trends: history Table 1. Channel characteristics of the instruments. fC is the central frequency of the channel (taken from Kleespies and Watts [2007]), Δf is the pass band width, NEΔT is the noise equivalent temperature from the first flight models (NOAA KLM User’s guide [Goodrum et al., 2007]). Nominal polarisations are for nadir view only and rotate with view angle. Ch. fC Δf Pass bands NEΔT Beam Width Polarisation [GHz] [GHz] [K] [deg] AMSU-B 1 89.0 0.5 1 0.37 1.1 V 2 150.0 1.0 2 0.84 1.1 V 3 183.3±1.0 0.5 2 1.06 1.1 V 4 183.3±3.0 1.0 2 0.70 1.1 V 5 183.3±7.0 2.0 2 0.60 1.1 V MHS 1 89.0 0.5 1 0.22 1.1 V 2 157.0 1.0 2 0.34 1.1 V 3 183.3±1.0 0.5 2 0.51 1.1 H 4 183.3±3.0 1.0 2 0.40 1.1 H 5 190.3 2.0 1 0.46 1.1 V
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Table 2. Mean NEΔT for the analysis time period, determined from the warm target views for all satellites. Units are in Kelvin. Ch. 1 2 3 4 5
2008-08 N15 0.33 0.71 2.32 1.38 1.10
2009-04/05 N16 0.37 0.74 3.76 2.58 3.67
N17 0.40 0.49 1.00 0.72 0.82
2009-09 MA 0.22 0.37 0.52 0.41 0.36
N18 0.22 0.39 0.58 0.44 0.35
N19 0.20 0.38 5.02 1.06 0.33
Paper III Simulating cloudy thermal infrared radiances with an optimised frequency grid in the radiative transfer model ARTS
Authors: G. Holl, S. A. Buehler, J. Mendrok, and A. Kottayil
To be submitted
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95 Simulating cloudy thermal infrared radiances with an optimised frequency grid in the radiative transfer model ARTS G. Holla , S. A. Buehlera , J. Mendroka , A. Kottayila a Division
of Space Technology, Department of Computer Science, Electrical and Space Engineering, Lule˚ a University of Technology, Rymdcampus 1, 98128 Kiruna, Sweden
Abstract This paper shows that cloudy infrared instrument radiances can be simulated with an optimised frequency grid derived under clear-sky conditions. For Highresolution Infrared Radiation Sounder (HIRS)/4 channel 11 (7.33 μm), cloudy Monte Carlo (MC) simulations using a previously clear-sky derived optimised frequency grid with 19 monochromatic pencil-beam simulations (mpbss) were compared with reference simulations using 4611 MPBS. For Advanced Very High Resolution Radiometer (AVHRR)/3 channel 5 (10.8 μm), a new optimised frequency grid was derived using clear-sky simulations, representing the channel with only 5 frequencies. Subsequently, cloudy simulations with the new optimised frequency grid were compared against simulations using a reference grid with 5461 MPBS. The root mean square error (RMSE) between the fast and the reference simulation was found to be less than 0.5 K for both comparisons, with the magnitude of the bias less than 0.03 K. The fast simulation is still more than 10 times faster than the reference simulation, even if the total number of photons to simulate a channel is the same. The findings will be used to statistically study the cloud signal in infrared radiances using the output of different general circulation models (GCMs). Those will be compared against collocations between AVHRR on-board National Oceanic and Atmospheric Administration (NOAA)18 and -19 and Cloud Profiling Radar (CPR) on-board CloudSat. The same will be carried out for microwave radiances. Finally, the aim is to derive an improved Ice Water Path (IWP) retrieval by combining Infra-Red (IR) and microwave (MW) radiances. Keywords: HIRS, AVHRR, radiative transfer, clouds, cloudy radiative transfer
1. Introduction Clouds are a major source of uncertainty in mankind’s understanding of the climate system [e.g. 24, Section 8.6.3.2]. This is particularly true for ice clouds. Email address:
[email protected] (G. Holl)
Preprint to be submitted to J. Quant. Spectrosc. Radiat. Transfer
December 1, 2011
96 Ice clouds have a complicated radiative feedback, depending on cloud altitude and poorly known microphysical properties. For this reason, both estimates of their climate feedback [27] and remote sensing of microphysical properties [28] are challenging. In estimates of the atmospheric column density of ice, Ice Water Path (IWP), models and measurements vary by up to an order of magnitude [33] and show different spatial distributions [12]. Therefore, there is a need for an improved IWP retrieval. Existing IWP products are based on visible/infrared [25, 17, 23], passive microwave [16] or active sensors [29, 30]. Active measurements may be augmented with coincident passive measurements. Clouds with IWP > 100 μm are opaque to infrared radiation [31, Figure 3.6]. Hence, IWP cannot be retrieved from infrared radiation alone. Ice particles smaller than 0.4 mm in diameter are transparent to microwave radiation at frequencies around 183 GHz, such as the humidity channels on Advanced Microwave Sounding Unit (AMSU)–B and Microwave Humidity Sounder (MHS) [33]. For thick clouds containing at least some particles visible at those frequencies, radiances can be accurately correlated to IWP. This is shown by Holl et al. [18] with the help of an Artificial Neural Network (ANN). However, many clouds are fully transparent at these frequencies and IWP can not always be retrieved from microwave radiation alone. Jim´enez et al. [19] have shown that sub-millimeter radiation, with frequencies higher than passive microwave but lower than infrared, can potentially be used to obtain an accurate retrieval of IWP. Space-borne instruments with sub-millimeter channels dedicated to the study of ice clouds have been proposed on multiple occasions [e.g. 4, 7] but no down-looking instrument is currently in orbit. Several limb-sounders operating in the sub-millimeter are currently in orbit and can used for IWP retrievals. Comparisons have been made by Eriksson et al. [14], Wu et al. [34], among others. However, none of these retrievals are operational and the limb-geometry is not optimal for climate monitoring, due to a poor spatial resolution. Active microwave, or RAdio Detection and Ranging (radar), probably provides the best estimate of IWP available to-date. At the time of writing, there is one such radar in orbit, the Cloud Profiling Radar (CPR) on-board Cloudsat [29]. Another radar is planned for launch on-board the EarthCare mission in 2012 [2]. A combination of infrared and passive microwave radiances may show better results than using only frequencies from either part of the spectrum alone. This combination is commonly exploited in rainfall retrievals [e.g. 22, 21]. Taylor and English [32] combine near-infrared and microwave to retrieve liquid cloud radiative and microphysical properties from instruments on a research aircraft. The synergy between infrared and passive microwave appears underutilised for the retrieval of ice microphysical parameters from satellite platforms. The present study is a first step towards better exploiting this synergy. As a first step to developing an IWP retrieval based on thermal infrared and passive microwave, we study how to prepare the radiative transfer model Atmospheric Radiative Transfer Simulator (ARTS) for the simulation of infrared 2
97 radiances, in order to study the IWP signal in passive radiances. This is the first time ARTS is used for the simulation of cloudy Infra-Red (IR) instrument radiances. ARTS is a physical model and cloudy simulations are much more expensive than clear-sky simulations. Buehler et al. [5] have shown that for the simulation of clear-sky High-resolution Infrared Radiation Sounder (HIRS) instrument radiances, an optimised frequency grid can be derived, so that a weighting of less than twenty monochromatic pencil-beam simulation (mpbs) gives approximately the same result as a weighting of several thousand mpbs. In this paper, we show that those optimised frequency grids can also be used to simulate cloudy radiances, dramatically reducing calculation time making a statistical study as described above practical. The setup of the paper is as follows. In section 2, we describe the sensors, the radiative transfer model and data input to the model. In section 3, we describe the experiments we have carried out to obtain a useable infrared setup for future cloudy simulations. The results of those experiments are presented in section 4. We finish by some concluding remarks and a discussion on future work. 2. Methodology As mentioned in the introduction, our aim so far is to show that an optimised frequency grid can be used to perform IR simulations using ARTS. First, we describe the instruments considered in this study. 2.1. Sensors For this study, we focus on operational sensors carried on meteorological satellites, because the aim is to develop an improved IWP retrieval that can be used for climate studies. Hence, sensors such as MODerate resolution Imaging Spectroradiometer (MODIS) will not be considered. The Advanced Very High Resolution Radiometer (AVHRR) is an imager in the visible/infrared that has been flown on polar-orbiting satellites from National Oceanic and Atmospheric Administration (NOAA) and MetOp since the late 1970s. It has a wide variety of atmospheric and non-atmospheric applications [10, 20]. On the latest generation, AVHRR/3, channels 4 (10.8 μm) and 5 (12 μm) are in the thermal infrared. The High-resolution Infrared Radiation Sounder (HIRS) is an infrared sounder for temperature and humidity dating back to the 1970s [26], currently in its 4th generation (HIRS/4). It carries twenty channels ranging from the visible up to 15 μm. It has been flown on polar-orbiting satellites in the Nimbus, Television InfraRed Operational Sounder (TIROS), NOAA and MetOp programmes, up to and including the most recent meteorological satellites, NOAA-19 and MetOp-A. A HIRS/4 footprint has a diameter of 10.2 km at nadir. The footprints are not contiguous.
3
98 2.2. Radiative transfer The Atmospheric Radiative Transfer Simulator (ARTS) is a physical model for the simulation of radiances at thermal infrared, sub-millimeter and microwave frequencies [15, 3]. ARTS is three-dimensional and fully polarised. It can perform either monochromatic pencil-beam simulations (mpbss), or convolve a spectrum with a sensor response function (SRF) and an antenna pattern. ARTS implements various optimisations to reduce calculation speed, without significantly compromising accuracy. The sensor response is efficiently modelled by a matrix multiplication [13]. Atmospheric absorption can be treated by an absorption lookup table [6]. For broadband radiometer simulations, such as the infrared sensors HIRS and AVHRR, a large number of radiances need to be calculated in order to fully characterise the instrument radiance. The spectrum thus calculated is convolved with the sensor response function to obtain a channel radiance. Buehler et al. [5] have developed a method to derive a small set of frequencies with associated weights that accurately represent the channel radiance. This allows the user to reduce the number of monochromatic radiance calculations from several thousand to less than twenty. This in turn dramatically decreases the calculation time without introducing a significant error in the calculated channel radiance. It becomes possible to simulate sufficiently many atmospheres to get good statistics. Buehler et al. [5] have derived optimised frequency grids for HIRS and for clear-sky cases only. We show that the optimised grid produces the same result as the reference grid, even for cloudy simulations. This is described in more detail further down. 2.2.1. Cloudy simulations ARTS is able to perform radiance simulations in the presence of scattering particles, such as ice particles. Two modules for calculating cloudy radiances are included. One is the Discrete Ordinate ITerative (DOIT) module. DOIT is a onedimensional, polarised, Discrete Ordinate Method (DOM). DOIT was developed for microwave and sub-millimeter radiances, where ice particle scattering phase functions are quite smooth. For infrared radiation, ice particle scattering phase functions have a strong forward peak [e.g. 8, 35]. To properly characterise this with a DOM, a very fine angular grid is required, which makes the simulation very slow and therefore impractical. Although methods exist to alleviate this problem, none are currently implemented in ARTS-DOIT. The other scattering module in ARTS is a backward Monte Carlo (MC) method [11]. MC is often slower than DOM, but in the presence of a strong forward peak, MC was found to be faster for the problem at hand. For each mpbs, a number of photons are generated and a radiance is calculated. This continues until either (1) a desired accuracy is reached, (2) a number of photons is reached, or (3) a time limit is reached. ARTS-MC can also include the antenna pattern, but this was not used in the present study. Only pencil-beam calculations were considered.
4
99 2.2.2. Atmospheric data To perform the simulations, we use a dataset developed by Chevallier et al. [9]. It contains a diverse set of atmospheric profiles, selected from reanalysis by the European Centre for Medium-range Weather Forecasting (ECMWF). We will refer to this as the Chevallier dataset. The dataset consists of several collections of 5000 profiles, each selected to maximise variability in a particular parameter: temperature, humidity, ozone, cloud condensate and precipitation. The total number of profiles is 25 000. For the derivation of the optimised AVHRR frequency grid, we used the dataset maximising cloud condensate. The Chevallier dataset contains mass densities for cloud ice water, cloud liquid water, precipitating ice (snow) and precipitating water (rain). It contains volume mixing ratios for water vapour and ozone. To accurately model infrared radiances, profiles for additional atmospheric gases are required. From the U.S. standard atmosphere given by Anderson et al. [1], we have obtained profiles for for carbon dioxide (CO2 ), nitrous oxide (N2 O), carbon monoxide (CO), methane (CH4 ), nitrogen (N2 ) and oxygen (O2 ). For those gases, we have used the same profile in every simulation. 2.2.3. Scattering data As mentioned before, ARTS needs single scattering properties from an external source. We use single scattering data for non-spherical ice particles as calculated by Yang et al. [35]. 3. Optimised infrared cloudy radiative transfer Buehler et al. [5] describe a mathematical method to derive an optimised frequency grid for a broadband radiometer channel. In the same paper, they apply this method to derive optimised grids for all thermal HIRS channels. In the present study, we apply the same method to derive an optimised grid for AVHRR channel 5. Buehler et al. [5] prove that their method works for the simulation of clear-sky radiances, but leave open the question if it works for the simulation of cloudy radiances. To find an answer to this question, we calculate radiances for a set of fifty cloudy atmospheres using both the reference grid and the fast grid. The number fifty was chosen as a compromise between calculation speed and sufficient statistics, because the simulation of cloudy radiances takes a long time (see also Table 2 on page 9). The atmospheres are from the Chevallier dataset [9] described earlier. We selected each 100th profile (profile number 0, 99, . . . , 4999) from the dataset maximising variability in cloud condensate. The dataset appears to be sorted incrementally by variability. Hence, choosing each 100th profile should provide an appropriate slice-through of the total variability represented by the 5000 profiles. For this test, we arbitrarily choose a particle shape of solid hexagonal spheres [35] and set surface emissivity to one. We calculate an optimised grid for AVHRR channel 5 (nominal wavelength 12.0 μm) on NOAA-19 (there are small differences in the SRFs between different 5
100 copies of AVHRR). ARTS uses frequency units for its radiative transfer calculations. The reference setup consists of a spectrum ranging from 23.5681 THz (12.72 μm; 786 cm−1 ) to 26.2981 THz (11.40 μm; 877 cm−1 ), with a constant grid spacing of 500 MHz (0.016 cm−1 ). In total, the reference grid is described by 5461 frequencies. We derive an optimised frequency grid so that the relative error in the spectral irradiance (in W m−2 Hz−1 sr−1 ) is at most 1 × 10−3 . The method to derive the optimised grid is described in detail by Buehler et al. [5]. Next, we test the newly derived reference grid for AVHRR-5 and the reference grid for HIRS-11 from Buehler et al. [5]. The number of frequencies for each grid is given in Table 1. The fast setup consists of 100 photons per mpbs for HIRS and 1000 photons per mpbs for AVHRR, corresponding to a total number of 1900 respectively 5000 photons for the channel radiance. For both sensors, the reference setup simulation uses 10 photons per mpbs, corresponding to 46 110 photons for HIRS and 54 610 photons for AVHRR. Each simulation is carried out ten times. Finally, we investigate the performance of both the reference and the fast setup for different numbers of photons. We repeat each simulation ten times with identical input, in order to determine runtimes and variability between different runs. We do so for different numbers of photons for the fast and the reference setup, in order to choose what configuration we want to use for future simulation studies. 4. Results 4.1. Infrared setup We find that AVHRR channel 5 can be accurately represented using a set of only 5 frequencies. In Figure 1, the green bars show the frequencies and associated weights that accurately represent the channel radiance. sensor AVHRR HIRS
photons
channel 5 11
fast
reference
5 19
5461 4611
Table 1 – Overview of number of frequencies for the fast and the reference frequency grids
Figure 2 shows a scatterplot between the reference runs and the fast runs. The figure includes the results for all runs: ten times fifty atmospheres, so five hundred simulations on each axis. For AVHRR, the root mean square error (RMSE) between the fast and the reference setup is 0.315 K. The bias is very small at −0.032 K. Bias and RMSE are similarly small for the runs with HIRS. We conclude that the fast frequency grid can be used even in a cloudy atmosphere.
6
101 NOAA-19 AVHRR SRFs and ARTS-simulated opacity 102 channel 4
channel 5
101
1
opacity
0.8 10−1 0.6 10−2 0.4
Channel response weight
100
10−3 0.2
10−4 10−5 10
10.5
11
11.5
12
12.5
0 13
wavelength [μm] H2 O N2 O
O3 weights
CO2
Figure 1 – AVHRR SRFs for the thermal channels with opacities of selected gases and frequencies for the fast setup.
Even with the optimised grid, Monte Carlo simulations are expensive. In fact, since the number of photons per monochromatic pencil beam needs to be higher for the fast setup than for the reference grid, it is not a priori obvious that the fast setup is desirable, even if it gives the same mean result. Therefore, we investigate how many photons per monochromatic pencil beam we need to reduce the MC error to an acceptable level yet obtain a simulation runtime that allows for doing statistical analyses. By MC error, we mean the variability of the calculated brightness temperatures between subsequent runs with identical input. Figure 3 shows show the MC error for HIRS and AVHRR for a varying number of photons per mpbs. Unsurprisingly, the brightness temperatures converge and the variability goes down as the number of photons is increased. When using only five photons in total to simulate the channel radiance, the variability may be very large; indeed, standard deviations of more than 20 K are observed. With a total of fifty photons, standard deviations are reduced to less than 10 K, but are still unacceptably high. For the runs with many photons, the standard deviation
7
102 AVHRR
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bias 0.036 K RMSE 0.393 K
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Figure 2 – Comparison of simulations of 50 cloudy atmospheres for AVHRR channel 5 and HIRS channel 11 comparing the reference and the fast setup, as described in the text.
is hard to see from the figure, as it is close to 0. The highest standard deviation for the AVHRR runs for the 50 selected atmospheres is 1.972 K for the runs with 500 photons and 0.666 K for the run with 5000 photons. A standard deviation of 2 K is still rather high, but a standard deviation of 0.666 K is acceptable for the purpose of this study. The standard deviations for the AVHRR reference setup with 5461 photons in total (1 per mpbs) are similar to those for the fast setup with 5000 photons. The HIRS runs show a similar pattern. In practice, the MC error is not the only consideration for choosing the setup. To get good statistics, a large number of scenarios need to be simulated. Therefore, the runtime per simulation is of major practical importance. Table 2 shows the time the simulations took to run on a Intel(R) Xeon(R) X5482 Dual QuadCore with 3.20 GHz CPU and 16 GiB RAM. It shows that runtime increases with the number of photons, but not quite linearly in the studied range. For a small number of photons per mpbs, runtime increases less than linearly with the number of photons, particularly when the number of frequencies to simulate is large. For approximately the same total number of photons (5000), the fast setup is still much faster than the reference setup. For the reference setup with 1 photon per mpbs, the CPU time is only slightly larger than the user time, suggesting a considerable overhead in the unparallelised part of the code. Therefore, it is still desirable to use the fast setup, even if the total number of photons required to reach a certain accuracy may be higher. The time difference between 5000 photons distributed over a large number of frequencies or the same number distributed over a small number of frequencies can be explained by the overhead associated with preparing the MC simulation for each mpbs. Some tasks, such as extracting optical properties, need to be performed once for each frequency. Therefore, we expect that this time difference holds not only for ARTS-MC, but also for other models.
8
103 photons
time
run MPBS
user
total
cpu
min
median
max
min
median
max
fast
1 10 100 1 000
5 50 500 5 000
39 s 4m 19 m 3h
43 s 4m 36 m 3h
50 s 4m 39 m 6h
2m 12 m 2h 15 h
2m 13 m 2h 15 h
2m 14 m 2h 20 h
reference
1 10
5 461 54 610
74 h 77 h
74 h 77 h
75 h 82 h
97 h 238 h
97 h 239 h
105 h 266 h
Table 2 – Time to simulate 50 cloudy atmospheres for AVHRR channel 5 using ARTS-MC on a Intel® Xeon®X5482 Dual QuadCore with 3.20 GHz (8 CPUs) and 16 GiB RAM. In the table, mpbs refers to a monochromatic pencil-beam simulation. “s” is seconds, “m” is minutes, and “h” is hours.
5. Conclusions and outlook In this study, we have shown that an optimised frequency grid derived for clear-sky conditions with the method described by Buehler et al. [5] can be applied for cloudy simulations. For a newly derived optimised frequency grid for AVHRR channel 5 and a frequency grid derived by Buehler et al. [5] for HIRS channel 11, we have investigated the performance of the ARTS-MC algorithm and studied how the choice of the number of photons affects standard deviations and runtimes. The results are highly useful for further studies. Like the optimised HIRS frequency grids developed by Buehler et al. [5], the new optimised frequency grid for AVHRR channel 5 is available for public use. We intend to apply the results to a systematic study of the IWP signal in AVHRR thermal radiances. We will compare statistics with those from a collocated dataset based on Holl et al. [18] and those for microwave radiances, in particular MHS channels around the 183 GHz water vapour absorption line. Ultimately, the aim is to use those statistics to obtain an improved IWP retrieval. Acknowledgements The position of the main author and PhD student is funded by the Swedish Vetenskapsr˚ adet. Thanks to Ping Yang for providing the authors with updated single scattering data for the infrared. We thank the UK MetOffice for providing the AAPP package and the ARTS radiative transfer community for its work on ARTS. We would also like to thank the National Graduate School in Space Technology at Lule˚ a University of Technology for offering courses and workshops that help the PhD student and first author in his research. [1] Anderson, G. P., Clough, S. A., Kneizys, F. X., Chetwynd, J. H., and Shettle, E. P.: AFGL atmospheric constituent profiles (0–120 km), Tech. rep., AFGL, TR-86-0110, 1986. 9
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HIRS-11 fast no. of photons test
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260 240 220 200 1 (19)
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0.4 0.3 0.2 0.1 0
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Figure 3 – Variability of brightness temperatures for ten times fifty cloudy simulations as described in the text. For each panel, the top sub-panel shows the range of brightness temperatures and the lower panel shows the standard deviation for ten runs with identical input (except for the seed of the random number generator). The legend shows the number of photons per frequency and in total.
14
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AVHRR-5 fast no. of photons test
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Chevallier profile number AVHRR-5 ref no. of photons test
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280 260 240 220 200
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1 (5461)
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0.4 0.2 0
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Chevallier profile number
Figure 4 – As Figure 3, but for AVHRR.
15
The end.
